This document contains a question bank with 370 questions related to digital signal processing. The questions cover topics such as signals and systems, sampling theory, analog to digital conversion, and signal properties. The questions range from definitions and short explanations to mathematical problems involving integrals, summations, and signal analysis. The document is intended as a study guide for a digital signal processing course taught by Dr. Nilesh Bhaskarrao Bahadure.
Digital signal processing involves processing digital signals using digital computers and software. There are several types of signals that can be classified based on properties like being continuous or discrete in time and value, deterministic or random, and single or multichannel. Common signals include unit impulse, unit step, and periodic sinusoidal waves. Signals can also be categorized as energy signals with finite energy, power signals with finite power, and even/odd based on their symmetry. Digital signal processing is used in applications like speech processing, image processing, and more.
This document discusses MOS transistor theory and provides examples for calculating threshold voltage (VT).
[1] It describes the basic structure of an n-channel MOSFET and the energy band diagrams for different biasing conditions, including accumulation, depletion, and inversion.
[2] Threshold voltage depends on factors like gate material, oxide thickness, channel doping, and interface charges. An example calculates VT0 = 0.38V for an nMOS transistor with given parameters.
[3] Body effect is explained, where threshold voltage increases with reverse substrate bias. An example plots VT as a function of VSB, using the body effect coefficient γ = 0.85V1/2 calculated for the
RF Circuit Design - [Ch2-1] Resonator and Impedance MatchingSimen Li
1) The document discusses resonators and impedance matching using lumped elements. It describes series and parallel resonant circuits, quality factor, bandwidth, and loaded/unloaded Q.
2) It also covers two-element L-shaped impedance matching networks for matching a load impedance to a source impedance. Methods for determining the reactance and susceptance values are presented for cases where the source impedance is less than or greater than the load impedance.
3) The goal of impedance matching is to maximize power transfer by making the impedances seen looking into the matching network equal to the source or transmission line impedance.
The presentation covers sampling theorem, ideal sampling, flat top sampling, natural sampling, reconstruction of signals from samples, aliasing effect, zero order hold, upsampling, downsampling, and discrete time processing of continuous time signals.
Stick Diagram and Lambda Based Design RulesTahsin Al Mahi
This presentation discusses stick diagrams and lambda-based design rules for VLSI system design. It begins with an overview of the top-down design hierarchy and then defines stick diagrams as a way to represent different layers of a layout using colors or monochrome lines. Common stick encodings are presented along with examples of drawing a CMOS inverter. Design rules are then covered, with lambda serving as a size-independent unit and rules specifying dimensions for wires, transistors, and contacts between layers. The goal is to convey key layer information and spacing requirements for mask layouts in a standardized way.
The document discusses the frequency response of amplifiers and how different circuit elements affect gain and phase shift at different frequencies. It introduces several key concepts:
1. The input, output, and bypass circuits each form RC networks that attenuate gain and introduce phase shift at lower frequencies.
2. The critical frequency is where gain drops by 3 dB (-3 dB point) and occurs when the capacitive reactance equals the resistance in each RC network.
3. Gain rolls off at -20 dB per decade below each critical frequency. Phase shift also increases at lower frequencies through each RC network.
4. Miller's theorem is used to analyze the effect of internal transistor capacitances at higher frequencies. The
Introduction
Band Pass Amplifiers
Series & Parallel Resonant Circuits & their Bandwidth
Analysis of Single Tuned Amplifiers
Analysis of Double Tuned Amplifiers
Primary & Secondary Tuned Amplifiers with BJT & FET
Merits and de-merits of Tuned Amplifiers
This document discusses several digital signal processing applications:
1) A two-band digital crossover system that splits an audio signal into low and high frequencies to be played through different speakers.
2) An ECG system that uses notch filters to remove 60Hz interference from power lines and allow detection of heart rate.
3) Speech noise reduction and coding systems that compress speech signals for transmission.
4) The compact disc recording and playback system which uses anti-aliasing filters, sampling, quantization, encoding, and laser etching to store digital audio that is then reconstructed through decoding, interpolation, DAC, and filtering.
Digital signal processing involves processing digital signals using digital computers and software. There are several types of signals that can be classified based on properties like being continuous or discrete in time and value, deterministic or random, and single or multichannel. Common signals include unit impulse, unit step, and periodic sinusoidal waves. Signals can also be categorized as energy signals with finite energy, power signals with finite power, and even/odd based on their symmetry. Digital signal processing is used in applications like speech processing, image processing, and more.
This document discusses MOS transistor theory and provides examples for calculating threshold voltage (VT).
[1] It describes the basic structure of an n-channel MOSFET and the energy band diagrams for different biasing conditions, including accumulation, depletion, and inversion.
[2] Threshold voltage depends on factors like gate material, oxide thickness, channel doping, and interface charges. An example calculates VT0 = 0.38V for an nMOS transistor with given parameters.
[3] Body effect is explained, where threshold voltage increases with reverse substrate bias. An example plots VT as a function of VSB, using the body effect coefficient γ = 0.85V1/2 calculated for the
RF Circuit Design - [Ch2-1] Resonator and Impedance MatchingSimen Li
1) The document discusses resonators and impedance matching using lumped elements. It describes series and parallel resonant circuits, quality factor, bandwidth, and loaded/unloaded Q.
2) It also covers two-element L-shaped impedance matching networks for matching a load impedance to a source impedance. Methods for determining the reactance and susceptance values are presented for cases where the source impedance is less than or greater than the load impedance.
3) The goal of impedance matching is to maximize power transfer by making the impedances seen looking into the matching network equal to the source or transmission line impedance.
The presentation covers sampling theorem, ideal sampling, flat top sampling, natural sampling, reconstruction of signals from samples, aliasing effect, zero order hold, upsampling, downsampling, and discrete time processing of continuous time signals.
Stick Diagram and Lambda Based Design RulesTahsin Al Mahi
This presentation discusses stick diagrams and lambda-based design rules for VLSI system design. It begins with an overview of the top-down design hierarchy and then defines stick diagrams as a way to represent different layers of a layout using colors or monochrome lines. Common stick encodings are presented along with examples of drawing a CMOS inverter. Design rules are then covered, with lambda serving as a size-independent unit and rules specifying dimensions for wires, transistors, and contacts between layers. The goal is to convey key layer information and spacing requirements for mask layouts in a standardized way.
The document discusses the frequency response of amplifiers and how different circuit elements affect gain and phase shift at different frequencies. It introduces several key concepts:
1. The input, output, and bypass circuits each form RC networks that attenuate gain and introduce phase shift at lower frequencies.
2. The critical frequency is where gain drops by 3 dB (-3 dB point) and occurs when the capacitive reactance equals the resistance in each RC network.
3. Gain rolls off at -20 dB per decade below each critical frequency. Phase shift also increases at lower frequencies through each RC network.
4. Miller's theorem is used to analyze the effect of internal transistor capacitances at higher frequencies. The
Introduction
Band Pass Amplifiers
Series & Parallel Resonant Circuits & their Bandwidth
Analysis of Single Tuned Amplifiers
Analysis of Double Tuned Amplifiers
Primary & Secondary Tuned Amplifiers with BJT & FET
Merits and de-merits of Tuned Amplifiers
This document discusses several digital signal processing applications:
1) A two-band digital crossover system that splits an audio signal into low and high frequencies to be played through different speakers.
2) An ECG system that uses notch filters to remove 60Hz interference from power lines and allow detection of heart rate.
3) Speech noise reduction and coding systems that compress speech signals for transmission.
4) The compact disc recording and playback system which uses anti-aliasing filters, sampling, quantization, encoding, and laser etching to store digital audio that is then reconstructed through decoding, interpolation, DAC, and filtering.
This document describes an R-2R ladder digital-to-analog converter (DAC). It explains that an R-2R ladder DAC uses only two resistor values, R and 2R, to convert a binary input signal into an analog output voltage. The circuit diagram and working of the R-2R ladder is provided. A 4-bit R-2R ladder DAC is simulated showing the output combinations. Advantages like only needing two resistor values and ability to expand bits are discussed. Applications like audio amplifiers and motor control are also listed.
Microwave hybrid circuits consist of microwave devices connected to transmit microwave signals as desired. Common microwave junction components include waveguide tees like E-plane, H-plane, and magic tees. Microwave networks were traditionally characterized using H, Y, and Z parameters, but S parameters became more common at microwave frequencies since they describe traveling waves. Key microwave components also include directional couplers, waveguide corners, bends, and twists which are used to change the guide direction while minimizing reflections.
This tutorial tries to define and describe the concept of Auto and Cross Correlation and how to calculate the coefficients. The procedure for finding the auto and cross correlation coefficients are described with examples.
This document discusses transmission line propagation coefficients including reflection coefficient and transmission coefficient. It defines the reflection coefficient as the ratio of reflected to incident voltage or current. Reflection and transmission coefficients are derived for a transmission line terminated by a load impedance. Standing wave patterns on transmission lines are also analyzed. Key properties of standing waves include maximum and minimum voltages occurring at intervals of half wavelength and voltages/currents being 90 degrees out of phase.
This document summarizes key aspects of the discrete Fourier transform (DFT). It defines the DFT, provides the formula for calculating it, and explains that the DFT transforms a discrete-time signal from the time domain to the frequency domain. It also outlines several important properties of the DFT, including linearity, shift property, duality, symmetry, and circular convolution. Examples are provided to illustrate duality and symmetry. References for further information on the discrete Fourier transform are also included.
The document discusses different types of linear-beam microwave tubes, specifically focusing on klystron tubes. It provides details on the operation of two-cavity klystrons and reflex klystrons. Two-cavity klystrons work by velocity modulating electrons in the first cavity which become current modulated before interacting with the second cavity to produce microwave power. Reflex klystrons use a single cavity and repeller field to reflect electrons, allowing them to interact twice with the cavity field and function as an oscillator. Quantitative analyses of velocity modulation, power output, and efficiency are also presented.
MMICs (Monolithic Microwave Integrated Circuits) are integrated circuits that operate at microwave frequencies between 300 MHz and 300 GHz. They are built on a single crystal and perform functions like microwave mixing, power amplification, and high frequency switching. MMICs are small, mass producible, and easier to use than hybrid circuits since they do not require external matching networks. They have advantages like low cost, small size, high reliability, and improved reproducibility. Some applications of MMICs include communications, homeland security scanners, imaging and sensors, and new areas like automotive radar and aircraft systems.
This document discusses transmission lines and the conditions required for distortionless transmission. It notes that losses in transmission lines can occur due to I2R loss, skin effect, and crystallization. Distortion can arise from amplitude distortion, attenuation distortion, and phase distortion. The conditions for distortionless transmission are that the attenuation constant must be zero and the phase velocity must be independent of frequency. This requires that the line's inductance and capacitance per unit length satisfy LG/RC=1/2. The document also examines propagation constants and phase velocity for lossless transmission lines. It provides examples of calculating phase velocity, propagation constant, and phase wavelength for given line parameters.
This document provides an overview of amplitude (linear) modulation techniques. It defines key concepts like modulation, baseband communication, and carrier communication. It then describes various amplitude modulation schemes including AM, DSB-SC, QAM, SSB, and VSB. Implementation and demodulation of these techniques is discussed. The document also covers frequency mixing, superheterodyne receivers, frequency division multiplexing, and carrier acquisition using phase-locked loops. Suggested problems are provided at the end.
Design of -- Two phase non overlapping low frequency clock generator using Ca...Prashantkumar R
This document describes designing a two-phase non-overlapping clock generator circuit with buffered outputs. The circuit is required to generate clean square wave clock signals from a single-phase input clock between 10-100MHz. The output signals must drive a 0.33pF capacitive load without distortion. The design will be implemented using Cadence tools and modified through simulation to meet the objectives of generating true non-overlapping signals with at least 1ns of underlap that can operate over the specified frequency range and drive the required load.
This document discusses different realization topologies for discrete-time systems, including direct form I and II, cascaded, and parallel realizations. Direct form II represents systems using two transfer functions - one for the input-output relationship and one for the output of the first function to the overall output. It can reduce the number of multiplications compared to direct form I. Cascaded and parallel realizations decompose the transfer function into smaller factors or terms that are each realized as small direct form II subsystems, which are then cascaded or paralleled. Using second-order subsystems rather than first-order can avoid complex coefficients and reduce operations compared to cascading first-order subsystems. FIR filters with linear phase can be
This presentation explains about the introduction of Bode Plot, advantages of bode plot and also steps to draw Bode plot (Magnitude plot and phase plot). It explains basic or key factors used for drawing Bode plot. It also explains how to determine Magnitude, phase and slope for basic factors. It also explains how to determine stability by using Bode Plot and also how to determine Gain Crossover Frequency and Phase Crossover Frequency, Gain Margin and Phase Margin. It also explains drawing Bode plot with an example and also determines stability by using Bode Plot and also determines Gain Crossover Frequency and Phase Crossover Frequency, Gain Margin and Phase Margin.
The document describes experiments on generating and demodulating amplitude shift keying (ASK), phase shift keying (PSK), and frequency shift keying (FSK) signals using MATLAB.
For ASK, binary data is used to modulate a carrier signal by varying its amplitude. Demodulation recovers the data using an envelope detector. For PSK, binary data modulates the phase of a carrier signal. Demodulation correlates the signal with a reference carrier. For FSK, binary data determines the frequency of the carrier signal. Demodulation correlates the signal with two reference carriers and compares the results.
The MATLAB program for each modulation scheme generates test signals, plots the results, and recovers the data
1. Power dividers are microwave components that divide input power between output ports. Common types include T-junction, Wilkinson, and multi-section broadband dividers. T-junction dividers can be lossless or lossy. Wilkinson dividers provide isolation between output ports.
2. Directional couplers are 4-port networks that divide power between through and coupled ports. They use quarter-wave length lines and even-odd mode analysis. Voltage ratios define coupling factors. Multisection designs provide broadband operation.
3. Hybrids like the quadrature and ring hybrids are 90 or 180 degree hybrids based on symmetric/asymmetric port designs and even-odd mode analysis to provide specific scattering
The presentation gives basic insight into Information Theory, Entropies, various binary channels, and error conditions. It explains principles, derivations and problems in very easy and detailed manner with examples.
This document discusses the gradual channel approximation (GCA) MOS transistor model for strong inversion operation. It provides three equations to model the MOSFET current-voltage characteristics in the linear/triode region, saturation region, and includes channel length modulation. Diagrams and an example are provided to illustrate the transistor operation and equations in each region.
This document discusses circuit design processes, specifically stick diagrams and design rules. It provides objectives and outcomes for understanding stick diagrams, which convey layer information through color codes. Stick diagrams show relative component placement but not exact sizes or parasitics. The document defines rules for stick diagrams and provides examples. It also discusses lambda-based design rules that define minimum widths and spacings to prevent shorts and allows scalability. Design rules provide a compromise between designers wanting smaller sizes and fabricators requiring controllability.
The document discusses Module 02 which covers the uniform plane wave equation and power balance. It is a lecture by Awab Sir who can be contacted at www.awabsir.com or by phone at 8976104646. The document contains repetitive text promoting the instructor's website and contact information.
Design and Implementation of Area Optimized, Low Complexity CMOS 32nm Technol...IJERA Editor
A numerically controlled oscillator (NCO) is a digital signal generator which is a very important block in many Digital Communication Systems such as Software Defined Radios, Digital Radio set and Modems, Down/Up converters for Cellular and PCS base stations etc. NCO creates a synchronous, discrete-time, discrete-valued representation of a sinusoidal waveform. This paper implements the development and design of CMOS look up Table based numerically controlled oscillator which improves the performance, reduces the power & area requirement. The design is implemented with CMOS 32 nm Technology with Microwind 3.8 software tool. In addition, it can be used for analog circuit also enables the integration of complete system on chip. This paper also describes the design of a NCO which is of contemporary nature with reasonable speed, resolution and linearity with lower power, low area. For all about Pre Layout simulation has been realized using 32nm CMOS process Technology.
ECET 345 Week 1 Homework
1.Express the following numbers in Cartesian (rectangular) form.
2.Express the following numbers in polar form. Describe the quadrant of the complex plane, in which the complex number is located.
This document describes an R-2R ladder digital-to-analog converter (DAC). It explains that an R-2R ladder DAC uses only two resistor values, R and 2R, to convert a binary input signal into an analog output voltage. The circuit diagram and working of the R-2R ladder is provided. A 4-bit R-2R ladder DAC is simulated showing the output combinations. Advantages like only needing two resistor values and ability to expand bits are discussed. Applications like audio amplifiers and motor control are also listed.
Microwave hybrid circuits consist of microwave devices connected to transmit microwave signals as desired. Common microwave junction components include waveguide tees like E-plane, H-plane, and magic tees. Microwave networks were traditionally characterized using H, Y, and Z parameters, but S parameters became more common at microwave frequencies since they describe traveling waves. Key microwave components also include directional couplers, waveguide corners, bends, and twists which are used to change the guide direction while minimizing reflections.
This tutorial tries to define and describe the concept of Auto and Cross Correlation and how to calculate the coefficients. The procedure for finding the auto and cross correlation coefficients are described with examples.
This document discusses transmission line propagation coefficients including reflection coefficient and transmission coefficient. It defines the reflection coefficient as the ratio of reflected to incident voltage or current. Reflection and transmission coefficients are derived for a transmission line terminated by a load impedance. Standing wave patterns on transmission lines are also analyzed. Key properties of standing waves include maximum and minimum voltages occurring at intervals of half wavelength and voltages/currents being 90 degrees out of phase.
This document summarizes key aspects of the discrete Fourier transform (DFT). It defines the DFT, provides the formula for calculating it, and explains that the DFT transforms a discrete-time signal from the time domain to the frequency domain. It also outlines several important properties of the DFT, including linearity, shift property, duality, symmetry, and circular convolution. Examples are provided to illustrate duality and symmetry. References for further information on the discrete Fourier transform are also included.
The document discusses different types of linear-beam microwave tubes, specifically focusing on klystron tubes. It provides details on the operation of two-cavity klystrons and reflex klystrons. Two-cavity klystrons work by velocity modulating electrons in the first cavity which become current modulated before interacting with the second cavity to produce microwave power. Reflex klystrons use a single cavity and repeller field to reflect electrons, allowing them to interact twice with the cavity field and function as an oscillator. Quantitative analyses of velocity modulation, power output, and efficiency are also presented.
MMICs (Monolithic Microwave Integrated Circuits) are integrated circuits that operate at microwave frequencies between 300 MHz and 300 GHz. They are built on a single crystal and perform functions like microwave mixing, power amplification, and high frequency switching. MMICs are small, mass producible, and easier to use than hybrid circuits since they do not require external matching networks. They have advantages like low cost, small size, high reliability, and improved reproducibility. Some applications of MMICs include communications, homeland security scanners, imaging and sensors, and new areas like automotive radar and aircraft systems.
This document discusses transmission lines and the conditions required for distortionless transmission. It notes that losses in transmission lines can occur due to I2R loss, skin effect, and crystallization. Distortion can arise from amplitude distortion, attenuation distortion, and phase distortion. The conditions for distortionless transmission are that the attenuation constant must be zero and the phase velocity must be independent of frequency. This requires that the line's inductance and capacitance per unit length satisfy LG/RC=1/2. The document also examines propagation constants and phase velocity for lossless transmission lines. It provides examples of calculating phase velocity, propagation constant, and phase wavelength for given line parameters.
This document provides an overview of amplitude (linear) modulation techniques. It defines key concepts like modulation, baseband communication, and carrier communication. It then describes various amplitude modulation schemes including AM, DSB-SC, QAM, SSB, and VSB. Implementation and demodulation of these techniques is discussed. The document also covers frequency mixing, superheterodyne receivers, frequency division multiplexing, and carrier acquisition using phase-locked loops. Suggested problems are provided at the end.
Design of -- Two phase non overlapping low frequency clock generator using Ca...Prashantkumar R
This document describes designing a two-phase non-overlapping clock generator circuit with buffered outputs. The circuit is required to generate clean square wave clock signals from a single-phase input clock between 10-100MHz. The output signals must drive a 0.33pF capacitive load without distortion. The design will be implemented using Cadence tools and modified through simulation to meet the objectives of generating true non-overlapping signals with at least 1ns of underlap that can operate over the specified frequency range and drive the required load.
This document discusses different realization topologies for discrete-time systems, including direct form I and II, cascaded, and parallel realizations. Direct form II represents systems using two transfer functions - one for the input-output relationship and one for the output of the first function to the overall output. It can reduce the number of multiplications compared to direct form I. Cascaded and parallel realizations decompose the transfer function into smaller factors or terms that are each realized as small direct form II subsystems, which are then cascaded or paralleled. Using second-order subsystems rather than first-order can avoid complex coefficients and reduce operations compared to cascading first-order subsystems. FIR filters with linear phase can be
This presentation explains about the introduction of Bode Plot, advantages of bode plot and also steps to draw Bode plot (Magnitude plot and phase plot). It explains basic or key factors used for drawing Bode plot. It also explains how to determine Magnitude, phase and slope for basic factors. It also explains how to determine stability by using Bode Plot and also how to determine Gain Crossover Frequency and Phase Crossover Frequency, Gain Margin and Phase Margin. It also explains drawing Bode plot with an example and also determines stability by using Bode Plot and also determines Gain Crossover Frequency and Phase Crossover Frequency, Gain Margin and Phase Margin.
The document describes experiments on generating and demodulating amplitude shift keying (ASK), phase shift keying (PSK), and frequency shift keying (FSK) signals using MATLAB.
For ASK, binary data is used to modulate a carrier signal by varying its amplitude. Demodulation recovers the data using an envelope detector. For PSK, binary data modulates the phase of a carrier signal. Demodulation correlates the signal with a reference carrier. For FSK, binary data determines the frequency of the carrier signal. Demodulation correlates the signal with two reference carriers and compares the results.
The MATLAB program for each modulation scheme generates test signals, plots the results, and recovers the data
1. Power dividers are microwave components that divide input power between output ports. Common types include T-junction, Wilkinson, and multi-section broadband dividers. T-junction dividers can be lossless or lossy. Wilkinson dividers provide isolation between output ports.
2. Directional couplers are 4-port networks that divide power between through and coupled ports. They use quarter-wave length lines and even-odd mode analysis. Voltage ratios define coupling factors. Multisection designs provide broadband operation.
3. Hybrids like the quadrature and ring hybrids are 90 or 180 degree hybrids based on symmetric/asymmetric port designs and even-odd mode analysis to provide specific scattering
The presentation gives basic insight into Information Theory, Entropies, various binary channels, and error conditions. It explains principles, derivations and problems in very easy and detailed manner with examples.
This document discusses the gradual channel approximation (GCA) MOS transistor model for strong inversion operation. It provides three equations to model the MOSFET current-voltage characteristics in the linear/triode region, saturation region, and includes channel length modulation. Diagrams and an example are provided to illustrate the transistor operation and equations in each region.
This document discusses circuit design processes, specifically stick diagrams and design rules. It provides objectives and outcomes for understanding stick diagrams, which convey layer information through color codes. Stick diagrams show relative component placement but not exact sizes or parasitics. The document defines rules for stick diagrams and provides examples. It also discusses lambda-based design rules that define minimum widths and spacings to prevent shorts and allows scalability. Design rules provide a compromise between designers wanting smaller sizes and fabricators requiring controllability.
The document discusses Module 02 which covers the uniform plane wave equation and power balance. It is a lecture by Awab Sir who can be contacted at www.awabsir.com or by phone at 8976104646. The document contains repetitive text promoting the instructor's website and contact information.
Design and Implementation of Area Optimized, Low Complexity CMOS 32nm Technol...IJERA Editor
A numerically controlled oscillator (NCO) is a digital signal generator which is a very important block in many Digital Communication Systems such as Software Defined Radios, Digital Radio set and Modems, Down/Up converters for Cellular and PCS base stations etc. NCO creates a synchronous, discrete-time, discrete-valued representation of a sinusoidal waveform. This paper implements the development and design of CMOS look up Table based numerically controlled oscillator which improves the performance, reduces the power & area requirement. The design is implemented with CMOS 32 nm Technology with Microwind 3.8 software tool. In addition, it can be used for analog circuit also enables the integration of complete system on chip. This paper also describes the design of a NCO which is of contemporary nature with reasonable speed, resolution and linearity with lower power, low area. For all about Pre Layout simulation has been realized using 32nm CMOS process Technology.
ECET 345 Week 1 Homework
1.Express the following numbers in Cartesian (rectangular) form.
2.Express the following numbers in polar form. Describe the quadrant of the complex plane, in which the complex number is located.
This document contains homework assignments, lab objectives, and reading materials for ECET 345 over 7 weeks. It includes questions on topics like Fourier analysis, Laplace transforms, sampling, discrete signals and systems, and convolution. Students are asked to work problems, write code in MATLAB, and analyze signals in both time and frequency domains. Readings are provided to introduce concepts covered in later assignments and labs.
Ecet 345 Enthusiastic Study / snaptutorial.comStephenson34
ECET 345 Week 1 Homework
1.Express the following numbers in Cartesian (rectangular) form.
2.Express the following numbers in polar form. Describe the quadrant of the complex plane, in which the complex number is located.
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
This document provides an overview of an advanced digital signal processing lecture. It discusses pre-requisites for the course including basic signals and communications knowledge and MATLAB proficiency. It outlines the course structure, including chapters covered, textbook references, and assessment breakdown. Key concepts from the first lecture are summarized such as characterizing signals as continuous or discrete, common signal representations including exponentials and sinusoids, and introducing linear time-invariant systems.
Design and analysis of dual-mode numerically controlled oscillators based co...IJECEIAES
In this paper, the design and analysis of dual-mode numerically controlled oscillators (NCO) based controlled oscillator frequency Modulation is implemented. Initially, input is given to the analog to digital converter (ADC) converter. This will change the input from analog to digital converter. After that, the pulse skipping mode (PSM) logic and proportional integral (PI) are applied to the converted data. After applying PSM logic, data is directly transferred to the connection block. The proportional and integral block will transfer the data will be decoded using the decoder. After decoding the values, it is saved using a modulo accumulator. After that, it is converted from one hot residue (OHR) to binary converter. The converted data is saved in the register. Now both data will pass through the gate driver circuit and output will be obtained finally. From simulation results, it can observe that the usage of metal oxide semiconductor field effect transistors (MOSFETs) and total nodes are very less in dual-mode NCO-based controlled oscillator frequency modulation.
FWSC UNIT-5 SYNCHRONIZATION OF DIRECT SEQUENCE SPREAD SPECTRUM SIGNALS.pdfMariyadasu123
This document summarizes a student project on synchronization of direct sequence spread spectrum signals. It includes an introduction to spread spectrum communication systems and direct sequence spread spectrum signals. It describes pseudonoise sequences, their properties, and types. It discusses code synchronization techniques including matched filter acquisition and serial search acquisition. It also describes code tracking using delay locked loops and tau-dither loops. The student implemented an acquisition system in MATLAB and analyzed the results.
This document describes a proposed project on multilevel inverter simulation and fault classification. It begins with an introduction on the importance of fault identification in electrical systems. A literature review is then presented covering previous work on fault detection techniques using methods like Concordia transforms and neural networks. The document outlines the proposed work, which includes simulating different types of multilevel inverters and extracting features to train a neural network for fault classification. Procedures for feature extraction, neural network training and testing are described. Future work is noted to expand the simulations and fault diagnosis to additional inverter configurations.
This document describes the design of an equal split Wilkinson power divider with the following specifications: frequency of 2.4 GHz, source and load impedances of 50 ohms, substrate permittivity of 3.38, substrate thickness of 1.524 mm, and conductor thickness of 0.15 mm. It provides background on Wilkinson power dividers, describes the calculation of microstrip line widths and lengths, shows the simulated circuit schematic and layout, and plots the resulting S-parameters which achieve the desired 3 dB power split with good port matching and isolation as expected.
This document contains a certificate certifying that a project report titled "ADVANCED INDO BORDER SECURITY SYSTEM" was submitted in partial fulfillment of the requirements for a Bachelor of Technology degree in Electronics and Communication Engineering at Dr. A.P.J. Abdul Kalam Technical University, Lucknow, India during the 2016-17 academic year. The project was carried out under the guidance and supervision of Ms. Kiran Kumari and Mr. Santosh Kumar Tripathi of B.N. College of Engineering and Technology, Lucknow.
The document discusses single carrier transmission using LabVIEW & NI-USRP. It covers several topics:
1. Symbol synchronization using the maximum output energy solution which introduces an adaptive element to find the optimal sampling time that maximizes output power.
2. The role of pseudo-noise sequences in frame synchronization, which provide properties like balance and unpredictability needed for random sequences.
3. The Moose algorithm for carrier frequency offset estimation and correction which exploits least squares to determine the phase shift between training sequences and correct sample phases.
4. The effects of multipath propagation including fading caused by constructive/destructive interference from multiple propagation paths, and intersymbol interference when path delays cause symbol interference.
The document discusses single carrier transmission using LabVIEW & NI-USRP. It covers several topics:
1. Symbol synchronization using the maximum output energy solution which introduces an adaptive element to find the optimal sampling time that maximizes output power.
2. The role of pseudo-noise sequences in frame synchronization, which provide properties like balance and unpredictability needed for random sequences.
3. The Moose algorithm for carrier frequency offset estimation and correction which exploits least squares to determine the phase shift between training sequences and correct sample phases.
4. The effects of multipath propagation including fading caused by constructive/destructive interference from multiple propagation paths, and intersymbol interference when path delays cause symbol interference.
Fundamentals of Digital Signal Processing - Question BankMathankumar S
This document contains questions related to the fundamentals of digital signal processing. It covers topics such as digital signal processing concepts, z-transforms, discrete Fourier transforms, digital filter design including IIR and FIR filters, and multi-rate signal processing. The questions range from conceptual definitions and properties to practical problems involving calculations and filter design. The document contains questions to test knowledge of key DSP topics and techniques.
REAL TIME ERROR DETECTION IN METAL ARC WELDING PROCESS USING ARTIFICIAL NEURA...IJCI JOURNAL
Quality assurance in production line demands reliable weld joints. Human made errors is a major cause of
faulty production. Promptly Identifying errors in the weld while welding is in progress will decrease the
post inspection cost spent on the welding process. Electrical parameters generated during welding, could
able to characterize the process efficiently. Parameter values are collected using high speed data
acquisition system. Time series analysis tasks such as filtering, pattern recognition etc. are performed over
the collected data. Filtering removes the unwanted noisy signal components and pattern recognition task
segregate error patterns in the time series based upon similarity, which is performed by Self Organized
mapping clustering algorithm. Welder’s quality is thus compared by detecting and counting number of
error patterns appeared in his parametric time series. Moreover, Self Organized mapping algorithm
provides the database in which patterns are segregated into two classes either desirable or undesirable.
Database thus generated is used to train the classification algorithms, and thereby automating the real time
error detection task. Multi Layer Perceptron and Radial basis function are the two classification
algorithms used, and their performance has been compared based on metrics such as specificity, sensitivity,
accuracy and time required in training.
Biomedical Signals Classification With Transformer Based Model.pptxSandeep Kumar
The document summarizes research using a transformer model to classify biomedical signals, specifically EEG signals. Key points:
- A transformer model was used to classify EEG signals from epilepsy patients using statistical features extracted from wavelet decompositions of the signals.
- The model was tested on the Bonn and CHB-MIT EEG datasets, achieving accuracy above 97% on binary, tertiary and 5-class problems from the Bonn data and above 95% accuracy for individual patients in the CHB-MIT data.
- The transformer model outperformed previous methods like MLP, SVM, ANN and CNN in classifying the EEG signals, demonstrating its effectiveness for biomedical signal classification tasks.
This document outlines the objectives, outcomes, modules, textbook, and experiments for the course ECE4001 Digital Communication Systems.
The course objectives are to interpret various digital modulation techniques, analyze line coding techniques, and understand the role of baseband and spread spectrum transmission.
The course outcomes include comprehending sampling and quantization, applying knowledge of signal theory to modulation techniques, characterizing line codes, designing pulses for interference-free transmission, and describing digital modulation and spread spectrum systems.
The course consists of 8 modules covering topics such as sampling, quantization, pulse code modulation, line codes, baseband systems, bandpass modulation, spread spectrum, and contemporary issues. Evaluation includes assignments, quizzes,
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Total slides: 73
Universal Asynchronous Receiver Transmitter (UART)
Introduction to Serial Communication
Types of Transmission
Simplex Communication
Duplex Communication
Half Duplex Communication
Full Duplex Communication
Methods of Serial data Transmission
Synchronous serial data transfer
Asynchronous serial data transfer
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Programming of transmission byte serially
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Question Bank Digital Signal Processing
1. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 1
UNIT – I
1. What is Digital signal processing
2. What is signals
3. Explain differences between DSP and ASP
4. Explain the advantages of DSP
5. Explain the limitations of DSP
6. Explain the classification of signals
7. Explain elementary continuous time signals with suitable examples.
8. Explain elementary discrete – time signals with suitable examples.
9. Define system; explain classification of systems in details.
10. Explain in details the following with suitable example
1. Stable & Unstable system
2. Static & Dynamic System
3. Linear & non – linear system
4. Causal & Non – causal system
11. Explain time variant and time invariant system with suitable example.
12. Write short notes on the following
1. Energy and power signals
2. Even and odd signals
3. Periodic & Aperiodic signals
4. Causal & non – causal signals
13. Evaluate the following integrals
1. ∝
10
2. 3
3. sin 2
4. 3
5. 3 3
6. cos 1 sin
7.
14. Find the following summations
1. ∑ 2 sin 2
2. ∑
3. ∑ 1
4. ∑ 2 cos 2 1 sin 2
5. ∑ 1
15. Find the fundamental period T of the following continuous – time signals
1. X(t) =
2. X(t) = sin 50
Total Questions 370
2. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 2
3. X(t) = 20 cos 10
16. Find whether the following signals are periodic or not also find period of the signals
1. X(t) = 2 cos 10 1 sin 4 1
2. X(t) = cos 60 sin 50
3. X(t) = 2 u(t) + 2 sin 2t
4. X(t) = 3 cos 4 2 sin 2
5. X(t) = u(t) – ½
6. X(t) =
3 cos 17 2 sin 19
7. X(t) = u(t) – u (t‐10)
8. X(t) = cos sin
9. X(t) = 12
9 ^ 3
17. Find whether the following signals are periodic or not
1. cos 2
2.
3. sin 1
4.
5.
6. 12 cos 20
18. Find the fundamental period of the following signals
1. X(t) = 2 sin 3 1
3 sin 4 1
2. X(t) = sin
3. X(n) = sin 2 sin 6
4. X(n) =
19. Find the even and odd components of the following signals.
1. X(t) = cos sin cos . sin
2. X(n) = {‐2, 1, 2, ‐1, 3}
3. X(t) = sin 2 sin 2 sin cos
4. X(n) = {1, 0, ‐1, 2, 3}
20. Find which of the following signals are causal & non – causal?
1. X(t) =
2. X(t) =
3. X(t) = sinc
4. X(n) = 2
21. Sketch the following signals
1. 1
2. X(t) = 2 1
3. X(t) = 3 1
4. X(t) = 2
5. X(t) = 2
6. X(t) = 3
7. 2 3
8. 2 .
22. Obtain energy for the signal x(n) = where a < 1.
23. Determine the values of energy & power of the following signals. Find whether the signals are
power, energy or neither energy nor power signals.
1. X(n) =
2. X(n) =
3. X(n) = sin
4. X(n) =
24. Determine the power and RMS value of the signal
X(t) = cos )
25. Determine the power and RMS value of the following signals
1. X(t) = 5 cos 50
3. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 3
2. X(t) = 10 sin 50
16 cos 100
3. X(t) = 10 cos 5 cos 10
4. X(t) =
cos
5. X(t) =
26. Sketch the following signals and calculate their energies
1.
2. 15
3. cos 2 . . 2
27. Find which of the following signals are energy signals
1. 1
2. 2
3. 1
28. Find which of the following signals are energy signals, power signals, neither energy nor power
signals
1.
2.
3. cos
29. Find whether the following systems are dynamic or not
1. 2
2. 2
3.
30. Determine whether the system described by the difference equation is linear or not
1. 2
2. 4
31. Check whether the following systems are causal or non – causal
1.
2. 2
3. 2 2
4.
5.
6.
7. . 1
8.
9.
10. ∑
11. cos
32. Check whether the following systems are linear or not
1. 3
2. 2
3.
4. 2 .
5.
6. 2
7.
8.
9.
10.
11. 2
4. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 4
12. . cos
33. Determine whether the following systems are time – invariant or not
1.
2. . cos 50
3.
4.
5.
6. 2
7. 1
8. 1
34. Check whether the following systems are time – invariant
1.
2. 5
3. 10
4.
5. 1
1
6. sin
35. Check whether the following systems are
1. Static or dynamic
2. Linear or non – linear
3. Causal or non – causal
4. Time – invariant or time – variant
(i)
(ii)
2
(iii)
(iv) 1
(v) cos
(vi) 10
(vii) ∑
(viii)
(ix)
36. Determine which of the following signals are periodic
1. 1 sin 15
2. 2 sin 20
3. 3 sin √2
4. 4 sin 5
5. 5 1 2
6. 6 2 4
37. Show that the complex exponential signal x(t) = is periodic and its fundamental period is
2 /
38. Check whether each of the following signals is periodic or not. If a signal is periodic, find its
fundamental period.
1. cos sin √2
2. sin
3.
4.
5. cos
6. cos sin
7. cos
39. Determine the fundamental period of
(a) x t cos sin
(b) cos 2
40. Determine the even & odd component of
5. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 5
41. Show that the product of two even signals or of two odd signals is an even signal and that the
product of an even and an odd signal is an odd signal.
42. Determine the energy and power of the following signals
1. | |
2.
3.
43. Determine whether the following signals are energy signals, power signals or neither
1. , 0
2. cos
3.
4. 0.5
5. 2
44. Write short note on analog to digital converter.
45. Explain in details the sampling theorem, also explain nyquist rate criterion for the sampling of
the analog signal.
46. Construct the discrete time signal from the two analog sinusoidal signals shown below
1 cos 2 10
2 cos 2 50
Which are sampled at a rate Fs = 40 Hz.
47. If the continues – time signal
2 cos 400 5 sin 1200 6 cos 4400 2 sin 5200 is sampled at a 8
KHz rate generating the sequence x[n], also find x[n].
48. Determine the nyquist frequency and nyquist rate for the following sequence
(a) 50 cos 1000
(b) 20
(c) 5 5
49. Determine the nyquist rate for the analog signal given by
2 cos 50 5 sin 300 4 cos 100
50. The transfer of an ideal band pass filter is given by
1 45 60
= 0 otherwise
Determine the minimum sampling frequency to avoid aliasing.
51. Consider the analog signal
3 cos 100
(a) Determine the minimum sampling rate required to avoid aliasing
(b) Suppose that the signal is sampled at the rate Fs = 200 Hz. What is the discrete time signal
obtained after sampling?
(c) Suppose that the signal is sampled at the rate Fs = 75 Hz. What is the discrete time signal
obtained after sampling?
(d) What is the frequency 0 < F < Fs/2 of a sinusoid that yields samples identical to those
obtained in part (c)?
52. Consider the analog signal
6. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 6
3 cos 50 10 sin 300 cos 100
What is the nyquist rate for this signal?
53. Consider the analog signal
3 cos 2000 5 sin 6000 10 cos 12000
(a) What is the nyquist rate for this signal?
(b) Assume now that we sample this signal using a sampling rate Fs = 5000 samples/sec. what is
the discrete time signal obtains after sampling?
(c) What is the analog signal what we can reconstruct from the samples if we use ideal
interpolation?
54. Draw and explain analog to digital converter system, also explain in details the sampling process.
55. Explain the followings
(a) Sampling
(b) Quantization
(c) Encoding
56. Determine which of the following signals are periodic. If periodic determine the fundamental
period
1. 3
2. 1
3. 3 3 sin
4. ∑ 1 2
5. cos sin
57. Determine the energy and power of signal given by
1
2
0
3 n 0
58. Fine energy and power of the following signals
1.
2. 0
= 0 n < 0
59. Determine whether the following Discrete time systems are stable or not
1.
2. 6
3. cos
4.
5. 2
7. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 7
University Question Bank
(Electrical, EEE, Electronics)
1. (a) Name the different properties of the discrete time system.
(b) Differentiate between an energy and power signal. Also determine the energy and
power of the signal
(c) The discrete time system x(n) and y(n) are shown:
Sketch the signal 2 4
(d) State the sampling theorem.
A given analog signal is 2 cos 200 3 sin 600 8 cos 1200
1. Calculate the nyquist rate
2. If f(t) is sampled at a rate of fs = KHz. What is the discrete time signal?
1. (a) What are energy and power signals?
(b) Check whether the following systems are:
1. Static or dynamic
2. Causal or non – causal
3. Linear or non – linear
∑
1
(c) Consider the discrete time system is excited by following sequence:
1 0 3
= 0 elsewhere
Find out the response y[n] if x[n] and y[n] are related by following relation:
i.
ii. 1
iii. 1
iv. 1 1
8. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 8
(d) A discrete time signal is shown in figure – 1 carefully determines and sketch the
following signal
i. 2
ii. ∑
iii. 2 2
1. (a) Determine the Nyquist rate for the continuous time signal
6 cos 50 20 sin 300 10 cos 100
(b) (i) Decompose the discrete time signal x(n) shown into even and odd parts
(ii) A discrete time system is described by the following expression
1
Now a bounded input of x (n) = 2δ (n) is applied to this system. Assume that the system
is initially relaxed, check whether the system is stable or unstable.
(c) With illustration, explain shifting, folding and time scaling operations on the discrete
time signals.
(d) (i) Sketch the following signal
| |
0
Also determine the energy and power of the signal.
(ii) Explain if the following system described by sin 2
Is memoryless, causal, linear, time – invariant, stable
1. (a) Is the system described by the following equation stable or not? Why?
9. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 9
(b) (i) Determine whether or not each of the following signals is periodic. If a signal is
periodic, specify its fundamental period
1. 1
2. 3
3. 4 3
(ii) Determine the fundamental period of the signal 2 cos 10 1
sin 4 1
(c) (i) Show that the signal 1 is neither an energy nor a power
Signal
(ii) Check the causality of the given system
(a)
(b) cos 1
(d) (i) A discrete time system is characterized by the following difference equation:
1 Check the system for BIBO stability
(ii) Consider the system shown in figure. Determine whether it is
(a) Memoryless
(b) Causal
(c) Linear
(d) Time – invariant
(e) Stable
10. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 1
UNIT – II
1. Represent the sequence , , , , , , , as sum of shifted unit impulse.
2. Explain the properties of convolution
3. Explain causality of linear time ‐ invariant system
4. Explain the stability condition of linear time – invariant system
5. Finite duration sequence given as , , , resolve the sequence x(n) into sum of
weighted impulse.
6. Represent the sequence , , , , , as sum of shifted unit impulses.
7. Test the stability of the system whose impulse response
8. The impulse response of a linear time – invariant system is , , , determine
the response of the system to the input signal , , ,
9. Obtain linear convolution of following sequences
, , , , ,
10. Compute the convolution y(n) of the signals
,
,
,
11. Given
a. Plot x1(n) and x2(n)
b. Calculate and plot y(n) = x1(n) * x2(n) for all n
c. What are non – zero lengths of x1(n), x2(n) and y(n)
12. Prove and explain graphically the difference between relations:
a.
b. ∗
13. Obtain the expression for convolution of unit step sequence with finite duration sequence
14. Obtain linear convolution of two discrete time signals as
, 1
15. Use discrete convolution to find the response to the input of the LTI system
with impulse response
16. Impulse response of an LTI system is given as find the output y(n)
of the system to an input
17. Obtain linear convolution of the following sequence , , ,
, , ,
18. Obtain linear convolution of the discrete time signals
11. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 2
19. Determine the convolution sum of two sequences , , , ; , , ,
20. Digital filter is characterized by the difference equation check the
filter for BIBO stability
21. Check whether the following digital systems are BIBO stable or not
(a)
(b)
(c)
(d) −1)
(e) −1)
(f) , ,
(g) , ,
(h)
22. Check the BIBO stability for the impulse response of a digital system given by
23. Determine the range of values of parameters ‘a’ for the LTI system with impulse response
,
= 0 , otherwise
To be stable
24. Test whether the following system are stable or not.
(a)
(b) ∑
(c) | |
(d)
25. From the impulse response h(n) of the system, find whether the following systems are causal
and stable
(a)
(b)
(c)
(d) | |
26. Determine the impulse response for the cascade of two linear time – invariant systems having
impulse responses.
27. Determine the range of values of a and b for which the linear time – invariant system with
impulse response
,
, 0
13. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page 1
UNIT – II and III
2 Number Questions
1. Represent the sequence , , , , , , , as sum of shifted unit impulse.
2. Explain the properties of convolution
3. Explain causality of linear time ‐ invariant system
4. Explain the stability condition of linear time – invariant system
5. Finite duration sequence given as , , , resolve the sequence x(n) into sum of
weighted impulse.
6. Represent the sequence , , , , , as sum of shifted unit impulses.
7. Obtain linear convolution of following sequences
, , , , ,
8. What is convolution, explain with example
9. Prove that
10. Write short notes on homogeneous solution
11. Write short notes on particular solution
12. Write short notes on impulse response
13. Explain the importance of convolution
14. What is LTI System
15. Write the general difference equation for LTI system
16. Explain cascade and parallel interconnection method.
17. Show that the necessary and sufficient condition for a LTI system to be stable is
∑ | | ∞
Where is the impulse response?
18. The system shown in figure (a) is formed by connecting two systems in cascade. The impulse
responses of the system are given by and respectively and
, . Find the impulse response of the overall system shown in
figure (b)
14. Digital Signal Processing
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Long Answer Questions
1. Test the stability of the system whose impulse response
2. The impulse response of a linear time – invariant system is , , , determine
the response of the system to the input signal , , ,
3. Obtain linear convolution of following sequences
, , , , ,
4. Compute the convolution y(n) of the signals
,
,
,
5. Given
a. Plot x1(n) and x2(n)
b. Calculate and plot y(n) = x1(n) * x2(n) for all n
c. What are non – zero lengths of x1(n), x2(n) and y(n)
6. Prove and explain graphically the difference between relations:
7.
8. ∗
9. Obtain the expression for convolution of unit step sequence with finite duration sequence
10. Obtain linear convolution of two discrete time signals as
, 1
11. Use discrete convolution to find the response to the input of the LTI system
with impulse response
12. Impulse response of an LTI system is given as find the output y(n)
of the system to an input
13. Obtain linear convolution of the following sequence , , ,
, , ,
14. Obtain linear convolution of the discrete time signals
15. Determine the convolution sum of two sequences , , , ; , , ,
16. Find the convolution of the signals
, , ,
,
,
17. Find the convolution of two finite duration sequence
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i. When a
ii. When a = b
18. Find y(n) if x(n) = n + 2 for
19. Determine the response of the relaxed system characterized by the impulse response
to the input signal
20. Compute convolution of following sequences
(a) , ,
(b) ;
(c) ;
21. Find the convolution of two finite duration sequences
,
,
And
,
,
22. Find the convolution of the two signals shown below
23. Compute the convolution y(n) = x(n) * h(n) of the signals
, , , , , , ,
24. Digital filter is characterized by the difference equation check the
filter for BIBO stability
25. Check whether the following digital systems are BIBO stable or not
(a)
(b)
(c)
(d) −1)
(e) −1)
(f) , ,
(g) , ,
(h)
26. Check the BIBO stability for the impulse response of a digital system given by
27. Determine the range of values of parameters ‘a’ for the LTI system with impulse response
,
= 0 , otherwise
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To be stable
28. Test whether the following system are stable or not.
(a)
(b) ∑
(c) | |
(d)
29. From the impulse response h(n) of the system, find whether the following systems are causal
and stable
(a)
(b)
(c)
(d) | |
30. Determine the impulse response for the cascade of two linear time – invariant systems having
impulse responses.
31. Determine the range of values of a and b for which the linear time – invariant system with
impulse response
,
, 0
Is stable also check causality?
32. Determine the homogeneous solution of the system described by the 1st
order difference
equation
33. Determine the particular solution of the difference equation
When the forcing function , and zero elsewhere.
34. Determine the total solution , , to the difference equation
When x (n) is a unit step sequence [i.e. is the initial condition.
35. Determine the response , , of the system described by the 2nd
order difference
equation.
When the input sequence
36. Determine the impulse response h(n) for the system described by the second – order
difference equation
37. Determine the zero input response of the system described by the homogeneous 2nd
order
difference equation
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Also find the solution by assuming initial conditions
38. Find the natural response of the system described by difference equation
With initial condition
39. Find the natural response of the system described by difference equation
With initial condition
40. Find the forced response of the system described by difference equation
When the input is
41. Find the response of the system described by the difference equation
For the input , with initial conditions
42. Find the natural response of the system described by the difference equation
. . ; ,
43. Find the forced response of the system described by the difference equation
. . ;
44. For a given system
. . ; ,
Find the response due to the input
45. Find natural response with initial conditions y(‐1) = y(‐2) = 1 for the difference equation
46. Find the forced response for input for the difference equation
47. Find the response with initial conditions y(‐1) = y(‐2) = 1
48. Determine the impulse response h(n) for the difference equation
. .
49. Determine the impulse response h(n) for the difference equation
50. Determine the impulse response of the difference equation
(a)
(b)
(c) . .
51. Determine the step response of the system described by
52. Determine the natural response
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(a) ; ,
(b) ; ,
53. Find the forced response
(a)
(b)
54. Determine the step response
(a)
(b) . .
(c)
55. Find the solution to the difference equation
(a)
With initial conditions
(b)
With initial conditions
56. Find the natural response of the system described by difference equation
When the input is with initial condition
57. Determine the impulse response h(n) for the system described by the second – order
difference equation
. .
58. Determine the impulse response h(n) for the system described by difference equation
59. Determine the impulse response h(n) for the system described by the 2nd
order difference
equation
60. Find the impulse response and step response of a discrete – time linear time – invariant
system whose difference equation is given by
.
61. Find the impulse response and step response for the given system
62. Consider a causal and stable LTI system whose input x(n) and output y(n) are related through
the 2nd
order difference equation
Determine the impulse response of the system.
63. Find the step response of the system
64. Solve the difference equation
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For the input sequence
;
; 0
Assume the initial condition y(n) = 0 for n < 0
65. Find the response of the following difference equation
,
66. A system is described by the difference equation
. Assuming that the system is initially relaxed, determine its unit sample response.
67. Determine the solution of the difference equation
68. Obtain the frequency response of the first order system with difference equation
with initial condition and sketch it. Comment about its
stability.
69. Determine the impulse response h(n) for the system described by the 2nd
order difference
equation
70. Find the magnitude and phase responses for the system characterized by the difference
equation.
71. Find the impulse response, frequency response, magnitude response and phase response of
the 2nd
order system
72. The output y(n) for an LTI system to the input x(n) is
Compute and sketch the magnitude and phase of the frequency response of the system for
| |
73. Determine the frequency response, magnitude response, phase response and time delay of
the system given by
74. Find the magnitude response and impulse response of a system described the difference
equation
75. LTI system is described by . plot magnitude response of system using
analytical method.
76. Find the magnitude and phase response of given system at frequency
.
20. Digital Signal Processing
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Dr. Nilesh Bhaskarrao Bahadure
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UNIT – IV to VI
1. Explain discrete time Fourier transform, also explain the difference between the Fourier
transform and DTFT
2. Write short note on existence of Fourier transform / DTFT
3. What is discrete Fourier transform, show the equation using twiddle factor
4. What do you mean by twiddle factor.
5. Explain the properties of Discrete Fourier transform
6. Define the Parseval’s theorem.
7. Define zero padding, also explain the use of zero padding in discrete Fourier transform
calculation.
8. Explain why number of elements (N) is greater than or equal to the length of sequence (L) in
the calculation of discrete Fourier transform
9. Explain with suitable example why linear convolution and circular convolution is produced
different result.
10. Explain with suitable example how to generate same result using linear and circular
convolution.
11. Explain the differences between linear and circular convolution.
12. What is meant by radix – 2 FFT
13. What is decimation – in – time algorithm?
14. What is decimation – in – time algorithm?
15. Explain the differences between DIF and DIT algorithms
16. Explain in details the comparison between DFT and FFT.
17. Explain in details how the FFT algorithms are efficient method or less complex compared to
DFT.
18. Obtain DTFT of unit impulse (n)
19. Obtain DTFT of unit step
20. Find DTFT of
21. Find DTFT of
22. Find DTFT of
23. Obtain DTFT of
24. Obtain DTFT of left handed exponential signal
25. Obtain DTFT of a double sided exponential signal
26. Find DTFT of , , ,
27. Find the DTFT of the following finite duration sequence of length L
28. Obtain DTFT of a signal , 1
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29. Obtain DTFT and sketch the magnitude spectrum for
30. Find DTFT of .
31. Find DTFT of | |
32. Find discrete time signal for
–
DISCRETE FOURIER TRANSFORM
33. Find DFT of unit impulse
34. Obtain DFT of delayed unit impulse
35. Obtain N – point DFT of exponential sequence
36. Find 4 – point DFT of the following sequence , , ,
37. Find 4 – point DFT of the sequence
38. Determine the DFT of the sequence
(a)
,
,
(b)
,
39. Derive the DFT of the sample data sequence , , , , , and compute the
corresponding amplitude and phase spectrum
40. Find the 4 – point DFT of the function
41. Compute the DFT of
42. Compute N – point DFT of
43. Compute the DFT of the sequence given as
(a) N = 3
(b) N = 4
44. Obtain the value of for 8 – point DFT if , , , , , , ,
45. Determine and sketch the DFT of signal , , , ,
46. Determine 2 – point and 4 – point DFT of a sequence
Sketch the magnitude of DFT in the both the cases.
47. Obtain 2 – point and 4 – point DFT of
48. Calculate 8 – point DFT of , , ,
49. Find 8 – point DFT of , , ,
50. Find the sequence for which DFT given by , , ,
51. Find IDFT of the following sequence , , ,
52. Find IDFT of , , ,
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53. Find the inverse DFT of , , ,
CIRCULAR CONVOLUTION
54. Find the circular convolution of two sequences , , , , , ,
55. Find the circular convolution of two sequences , , , , , ,
56. Find the circular convolution of two sequences , , , , , ,
57. Find the linear and circular convolution of two sequences , , ,
, , ,
58. Using graphical method, obtain a 5 – point circular convolution of two DT signals defined as,
. ,
,
Does the circular convolution obtained is same to that of linear convolution?
59. Find circular convolution of two finite duration sequences
, , , , , , ,
60. Find the 8 point circular convolution for following sequences
, , , , , , ,
61. Compute the circular convolution of following sequences and compare the results with linear
convolution
, , , , , , , , , , , , , ,
62. Find the linear convolution of , , , ,
, , obtain the same result using circular convolution.
63. Let
,
,
find the circular convolution of the sequence
64. Compute (a) linear convolution (b) Circular convolution of the two sequences
, , , , , , . (c) also find the circular convolution using DFT & IDFT
65. Compute ∗ if
and
66. Obtain the linear convolution of two sequences defined as,
,
67. Using circular convolution, find output of system if input x(n) and impulse response h(n) given
by
68. Use the four point DFT and IDFT to determine the circular convolution of sequences
, , , , , ,
69. Find the response of an FIR filter with the impulse response , , to the input
sequence ,
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70. Determine the response of FIR filter using DFT if , ,
71. The first five points of the 8 – point DFT of a real valued sequence are . ,
. , , . . , determine the remaining three points.
72. The first five points of real and even sequence x(n) of length eight are given below. Find
remaining three points , , , , , , … … .
FAST FOURIER TRANSFORM
73. Given , , , , find X(k) using DIT FFT algorithm.
74. Given , , , , , , , find X(k) using DIT FFT algorithm
75. Given , , , , , , , find X(k) using DIT FFT algorithm
76. Given , find X(k) using DIT FFT algorithm.
77. Given , , , , , , , find X(k) using DIF FFT algorithm
78. Given , find X(k) using DIF FFT algorithm.
79. Given , find X(k) using DIF FFT algorithm.
80. Compute the DFT’s of the sequence , where N = 4, using DIF FFT algorithm.
81. Use the 4 – point inverse FFT and verify the DFT results {6, ‐2+j2, ‐2, ‐2‐j2}
82. Given
, . . , , . . , , . . , , .
. ,
83. Given , . . , , . . , , .
. , , . . ,
84. Given , . , , . , , . , ,
. ,
85. Determine DFT (8 – point) for a continuous time signal,
.
86. Develop a radix – 3 DIT FFT algorithm for evaluating the DFT for N = 9
87. Develop DIT FFT algorithms for decomposing the DFT for N = 6 and draw the flow diagram for
(a) N = 2.3 and
(b) N = 3.2
(c) Also, by using the FFT algorithm develop in part (b), evaluate the DFT values for
, , , , ,
88. Develop the DFT FFT algorithm for decomposing the DFT for N = 12 and draw the flow
diagram.
89. Develop a radix – 4 DIT FFT algorithm for evaluating the DFT for N = 16 and hence determined
the 16 – point DFT of the sequence.
, , , , , , , , , , , , , , ,
90. Develop a DIT FFT algorithm for decomposing the DFT for N = 6 and draw the flow diagrams
for
(a) N = 3.2 and
25. Digital Signal Processing
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Page 1
Filter Design
1. Determine frequency response of FIR filter defined by .
. . Calculate the phase delay and group delay.
2. Explain Fourier series method of designing FIR filters.
3. Design an ideal low pass filter with a frequency response
| |
Find the values of h (n) for N=11. Find H (z). Plot the magnitude response.
4. Design an ideal high pass filter with a frequency response
| |
| |
Find the values of h (n) for N=11. Find H (z). Plot the magnitude response.
5. Design an ideal band pass filter with a frequency response
| |
Find the values of h(n) for N=11. Find H (z). Plot the magnitude response.
6. Design an ideal band reject filter with a frequency response
| | | |
Find the values of h(n) for N=11. Find H (z). Plot the magnitude response.
7. Explain design of FIR filters using windows.
8. Explain Gibb’s Phenomenon.
9. Explain rectangular, Hanning and Hamming windows.
10. Design an ideal high pass filter with a frequency response
| |
| |
Find the values of h (n) for N=11. Design using Hanning Window. Plot the magnitude
response.
11. Design an ideal high pass filter with a frequency response
| |
| |
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18. Using a rectangular window technique design a Lowpass filter with passband gain of unity,
cutoff frequency of 1000 Hz and working at a sampling frequency of 5 KHz. The length of the
impulse response should be 7.
19. What is Gibb’s phenomenon?
Or
What are Gibb’s oscillations?
20. What are the desirable characteristics of the window?
21. Draw the impulse response of an ideal low pass filter.
22. What is the need for employing window technique for FIR filter design?
23. Use Fourier series method in conjunction with a Hamming window to design an
approximation to an ideal low pass filter with a magnitude response
| |
Compare the response with that obtained from an unwindowed design for N = 11.
24. Design an approximation to an ideal high pass filter with magnitude response
| |
By the Fourier series method with N = 11.
25. Explain the advantages of FIR filters over IIR filters.
26. The following transfer function characterizes an FIR filter (M=11). Determine the magnitude
response and also show that the phase delay and group delay are constant.
27. Design a Finite impulse response low pass filter with a cut – off frequency of 1 KHz and
sampling rate of 4 KHz with eleven samples using Fourier series
28. Determine the unit sample response of the ideal low pass filter. Why it is not realizable?
29. A low pass filter is to be designed with the following desired frequency response.
| |
Determine the filter coefficients if the window function is defined as
,
,
Also, determine the frequency response of the designed filter.
30. A filter is to be designed with the following desired frequency response
,
| |
Determine the filter coefficients if the window function is defined as
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,
,
Also, determine the frequency response of the designed filter.
31. Design a filter with
| |
Determine for M = 7 using a Hamming window.
32. Repeat above using rectangular window
(Ans: . . . .
33. Design a high pass filter using Hamming window with a cut off frequency of 1.2 rad/sec and N
= 9
(Hint: , )
34. Design an FIR digital filter to approximate an ideal low pass filter with passband gain of unity,
cut – off frequency of 850 Hz and working at a sampling frequency of . The
length of the impulse response should be 5. Use a rectangular window.
35. An FIR linear phase filter has the following impulse response.
,
,
Use Bartlett’s window and compute the impulse response of the filter. Find its magnitude and
phase response as a function of frequency.
36. Design a bandpass filter to pass frequencies in the range 1 ‐ 2 rad/sec using Hanning window
N=5
(Hint: ,
37. Design a bandpass filter which approximates the ideal filter with cut off frequency at 0.2
rad/sec and 0.3 rad/sec. the filter order is M = 7. Use the Hanning window function.
(Ans: , . , . , . , . ,
. , .
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1
Filter Realization
1. Obtain Direct form I/II and cascade form realization of a system transfer
function described by
y(n)-3/4 y(n-1)+1/8y(n-2)=x(n)+1/2x(n-1) PU Dec’00 NU S-98
2. Consider a causal LTI system with TF
H (z) = (1 + 1/5 Z-1
) / (1-0.5 Z-1
+ 1/3 Z-2
) (1+0.25 Z-1
)
Draw the signal flow graph for implementation of the system using Direct
form-II.
3. The TF is given by
H (z) = (1 – Z-1
) / (1-0.2 Z-1
-0.15 Z-2
)
Draw 1st
and 2nd
order cascade realization and parallel realization.
4. Develop parallel form realization
H (z) = (1 + 0.2 Z-1
+ Z-2
) / (1 – 0.75 Z-1
+ 0.125 Z-2
)
5. The system function for FIR filter is given as follows
H(z) = 1 – 3/2 Z-1
+ 3/2 Z-2
– Z-3
draw cascade realization.
= (1 – Z-1
) (1 – ½ Z-1
+ Z-2
)
6. y(n) = 2rcosw0y(n-1) – r2
y(n-2) + x(n) – rcosw0x(n-1) Draw Direct form I/II
structure.
7. Draw Direct form I/II realization of
H (z) = (1 + 0.2 Z-1
-0.2 Z-2
) / (1 – 0.2 Z-1
+ 0.3 Z-2
+ Z-3
)
8. Draw cascade form realization
H (z) = (Z/3 + 5/12 + 5/12 Z-1
+ Z-2
/12) / (1 – ½ Z-1
+ ¼ Z-2
)
Z/3 (1 + ¼ Z-1
) (1+Z-1
+Z-2
)
9. y(n) – ¾ y(n-1) + 1/8 y(n-2) = x(n) + 1/3 x(n-1) Draw cascde realization.
10. Draw cascade canonical IIR filter
H (z) = (1+Z-1
) / (1- Z-1
+ ½ Z-2
) (1-Z-1
+Z-2
)
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2
Digital filter design
Part – A: Impulse Invariance Method
1. Find out H(z) using Impulse invariance method (IIM) at 5Hz sampling
frequency from H(s) as given below
H(s) = 2 /(S+1)(S+2) PU May’2001
2. Using IIM with T=1sec determine H(z) if H(s) = 1/ (s2
+ √2 s +1)
3. Apply IIM and find H (z) for H(s) = (s+a) / [(s+a)2
+ b2
)].
4. Apply IIM and find H(z) for H(s) = b / [(s+a)2
+ b2
)]
5. An analog filter has a transfer function H(s) = 10 / (s2
+ 7s + 10) Design a
digital filter equivalent to this using IIM for T = 0.2 sec.
6. An analog filter has a transfer function H(s) = 5 / (s3
+ 6s2
+11s + 6) Design a
digital filter equivalent to this using IIM for T = 1 sec.
7. An analog filter has a transfer function H(s) = (s + 3) / (s2
+ 6s + 25) Design a
digital filter equivalent to this using IIM for T = 1 sec.
8. Determine H(z) using IIM for the system function PU Dec’2000
H(s) = 1 / (S+0.5)(S2
+ 0.5S + 2)
Part – B: Bilinear Transformation Method
9. The transfer function of analog filter is:
H(s) = 3 / (s+2) (s+3)
With Ts=0.1Sec Design digital IIR filter using BLT
10. Find out H(z) using BLT from H(s) as given below
H(s) = 2 /(S+1)(S+2) with T =1 sec
11. Determine H(z) using BLT is applied to
H(s) = (s2
+ 4.525) / (s2
+ 0.692s + 0.504).
12. An analog filter has a transfer function H(s) = 1 / (s2
+ 6s + 9) Design a digital
filter using BLT.
13. Design a single pole low pass filter with a 3dB bandwidth of 0.2π by use of
bilinear transformation applied to the analog filter.
H(s) = Ωc / (s + Ωc) where Ωc is the 3dB bandwidth of analog filter
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14. The system transfer function of A/F is given by
H(s) = (s+0.1) / [(s+0.1)2
+ 16]
Obtain the system transfer function of digital filter using BLT which is
resonant at w = π/2.
15. Use the bilinear transformation to convert the analog filter with the system
function. H (s) = (s + 0.1) / [(s + 0.1)2
+9]
into a digital IIR filter. Select T =0.1 sec and compare the location of the
zeroes in H (z) with the location of zeroes obtained by applying the impulse
invariance method in the conversion of H(s).
16. The Analog transfer function of low pass filter is
H(s) = 1 / (s+2) and its BW is 1 rad/sec. design the digital filter using BLT
method whose cut-off frequency is 20π and sampling time is 0.0167sec by
considering the warping method.
Part – C: Butterworth Low Pass Filter
17. Given the specification αp = 1dB, αs = 30dB, Ωp = 200 rad/sec, Ωs = 600
rad/sec. determine the order of the filter.
18. Determine the order and the poles of the Butterworth filter have 3dB
attenuation at 500Hz and an attenuation of 40dB at 1000Hz.
19. Prove that Ωc = Ωp / (100.1Ap
– 1)1/2N
= Ωs / (100.1As
– 1)1/2N
20. Determine the order and the poles of low pass Butterworth filter that has a
-3 dB bandwidth of 500 Hz and an attenuation of 40 dB at 1000 Hz.
21. Design an analog Butterworth filter that has a -2dB passband attenuation at
frequency of 20 rad/sec and at least -10dB stopband attenuation at 30 rad/sec.
22. For the given specification design an analog Butterworth filter.
0.9 ≤ | H(jΩ)| ≤ 1 for 0 ≤ Ω ≤ 0.2π. | H(jΩ)| ≤ 0.2 for 0.4π ≤ Ω ≤ π.
23. For the given specification find the order of the Butterworth filter αp = 3dB,
αs = 18dB, fp = 1KHz, fs = 2KHz.
24. For the given specification find the order of the Butterworth filter αp = 0.5dB,
αs = 22dB, fp = 10KHz, fs = 25KHz
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25. Find the pole location of a 6th
order Butterworth filter with Ωc = 1 rad/sec.
26. Design a 2nd
order low pass Butterworth filter with a cut – off frequency of
1KHz and sampling frequency of 104
samples/sec, by bilinear transformation.
27. Using bilinear transformation, design a Butterworth filter which satisfies the
following conditions.
0.8 ≤ | H (ejω
)| ≤ 1 for 0 ≤ ω ≤ 0.2π.
| H (ejω
)| ≤ 0.2 for 0.6π ≤ ω ≤ π.
28. Design low pass IIR filter is to be designed with Butterworth approximation
using BLT technique. Find the order of the filter to meet the following
specifications.
(i) Passband magnitude is constant within 1dB for frequencies below 0.2π
(ii) Stopband attenuation is greater than 15dB for frequencies between
0.3π to π.
29. An IIR low pass filter is required to meet the following specifications:
Passband peak to peak ripple : ≤ 1 dB
Passband edge : 1.2 KHz
Stopband attenuation : ≥ 40 dB
Stopband edge : 2.5 KHz
Sample rate : 8 KHz
The filter is to be designed by performing BLT on an analog system function
of required order of Butterworth filter so as to meet the specifications in the
implementation.
30. An IIR low pass filter is required to meet the following specifications:
Passband ripple : ≤ 1 dB
Passband edge : 4 KHz
Stopband attenuation : ≥ 40 dB
Stopband edge : 6 KHz
Sampling rate : 24 KHz
The filter is to be designed by performing BLT on an analog system function
of required order of Butterworth filter so as to meet the specifications in the
implementation.
31. An IIR low pass filter is required to meet the following specifications:
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Passband peak to peak ripple : ≤ 0.5 dB
Passband edge : 1.2 KHz
Stopband attenuation : ≥ 40 dB
Stopband edge : 2.0 KHz
Sample rate : 8 KHz
The filter is to be designed by performing BLT on an analog system function
of required order of Butterworth filter so as to meet the specifications in the
implementation.
Part – D: Chebyshev Filter
32. Given the specification αp = 3 dB, αs = 16 dB, fp = 1KHz, fs = 2KHz.
Determine the order of the filter using Chebyshev approximation. Find H (s).
33. Obtain an analog Chebyshev filter transfer function that satisfies the
constraints
1/√2 ≤ | H (jΩ)| ≤ 1 for 0 ≤ Ω ≤ 2
| H (jΩ)| ≤ 0.1 for Ω ≥ 4.
34. Determine the order of the filter and the poles of a type I low pass Chebyshev
filter that has a 1 dB ripple in the passband and passband frequency Ωp =
1000π , a stopband frequency of 2000π and an attenuation of 40 dB or more.
35. Design a Chebyshev filter with a maximum passband attenuation of 2.5 dB, at
Ωp = 20 rad/sec and stopband attenuation of 30 dB at Ωs = 50 rad/sec.
36. For the given specification find the order of the chebyshev – I filter αp = 1.5
dB, αs = 10dB, Ωp = 2 rad/sec, Ωs = 30 rad/sec.
37. Find the pole locations of a normalized chebyshev filter of order 5.
38. Design a Chebyshev filter for the following specification: αp = 1 dB, αs = 25
dB, Ωp = 1 rad/sec, Ωs = 20 rad/sec.
39. Determine the system function H (z) of the lowest order chebyshev digital
filter that meets the following specification.
(i) 1 dB ripple in the passband 0 ≤ |ω| ≤ 0.3π
34. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
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(ii) At least 60 dB attenuation in the stopband 0.35π ≤ |ω| ≤ π. Use the
bilinear transformation.
40. Determine the system function H (z) of the lowest order chebyshev digital
filter that meet the following specification.
(i) ½ dB ripple in the passband 0 ≤ |ω| ≤ 0.24π
(ii) At least 50 dB attenuation in the stopband 0.35π ≤ |ω| ≤ π. Use the
bilinear transformation.
Part – E Additional Examples:
41. Design a digital Butterworth filter satisfying the constraints
0.707 ≤ | H (ejω
)| ≤ 1 for 0 ≤ ω ≤ π/2.
| H (ejω
)| ≤ 0.2 for 3π/4 ≤ ω ≤ π.
With T=1 sec using (a) The bilinear transformation (b) Impulse invariance.
Realize the filter in each case using the most convenient realization form.
42. Design a Chebyshev low pass filter with the specification αp = 1 dB ripple in
the pass band 0 ≤ ω ≤ 0.2π, αs = 15 dB ripple in the stop band 0.3 π ≤ ω ≤ π,
using (a) Bilinear transformation (b) Impulse invariance.
43. Design a digital Butterworth filter satisfying the constraints
0.8 ≤ | H (ejω
)| ≤ 1 for 0 ≤ ω ≤ 0.2π.
| H (ejω
)| ≤ 0.2 for 0.6π ≤ ω ≤ π.
With T=1 sec using (a) The bilinear transformation (b) Impulse invariance.
Realize the filter in each case using the most convenient realization form.
44. Determine the system function H(z) of the lowest order Chebyshev and
Butterworth digital filter with the following specification
(a) 3 dB ripple in pass band 0 ≤ ω ≤ 0.2π.
(b) 25 dB attenuation in stop band 0.45π ≤ ω ≤ π.
45. Design a Chebyshev filter satisfying the constraints
0.8 ≤ | H (ejω
)| ≤ 1 for 0 ≤ ω ≤ 0.2π.
| H (ejω
)| ≤ 0.2 for 0.6π ≤ ω ≤ π.
With T=1 sec using (a) The bilinear transformation (b) Impulse invariance.
Realize the filter in each case using the most convenient realization form.
46.
35. Digital Signal Processing
Question Bank
Department of Electronics Engineering
Dr. Nilesh Bhaskarrao Bahadure
Page
7
47. Give the magnitude function of the Butterworth filter. What is the effect of
varying order of N on magnitude and phase response?
48. Give any two properties of Butterworth low pass filter
49. What are the properties of Chebyshev filter?
50. Give the equation for the order of N and cut off frequency ΩC of Butterworth
filter.
51. Give the Chebyshev filter transfer function and its magnitude response.
52. Distinguished between the frequency responses of Chebyshev type I filter for
N odd and N even.
53. Distinguished between the frequency response of Chebyshev type I and type
II filters.
54. Give the expression for the location of poles and zeros of a Chebyshev type II
filter.
55. Give the expression for the location of poles and zeros of a Chebyshev type I
filter.
56. Distinguished between Butterworth and Chebyshev type I filter.
57. Explain how one can design digital filters from analog filters?
58. Mention any two procedures for digitizing the transfer function of an analog
filter.
59. What are the properties that are maintained same in the transfer of analog
filter into digital filter?