The document provides an overview of principles of telecommunications. It discusses key topics like signals and systems, modulation techniques, noise in communication systems, and classification of signals. The document outlines the course EEB317 which will cover these topics in depth, including signals and systems, amplitude modulation, angle modulation, detection and demodulation. It provides brief descriptions of signals, systems, Fourier series, correlation, and other fundamental concepts in telecommunications.
Es400 fall 2012_lecuture_2_transformation_of_continuous_time_signal.pptxumavijay
This document outlines transformations that can be applied to continuous-time signals, including time reversal, time scaling, time shifting, and amplitude transformations. It also discusses properties of even and odd signals. Time reversal flips the signal across the time axis. Time scaling stretches or compresses the time axis. Time shifting slides the signal along the time axis. Amplitude transformations multiply the signal by a constant and add an offset. The product of two even signals is even, while the product of an even and odd signal is odd.
This document provides an introduction to signals and systems. It begins by classifying different types of signals as continuous-time/discrete-time, analog/digital, deterministic/random, periodic/aperiodic, power/energy. It then discusses representations of signals in the time and frequency domains, including the Fourier series representation of periodic signals. Key concepts covered include the unit step, rectangular, triangular and sinc functions, as well as signal operations like time shifting, scaling and inversion. The document concludes by introducing Parseval's theorem relating the power of a signal to the power of its Fourier coefficients.
This document provides an overview of signals and systems. It defines signals as functions that carry information over time or discrete steps. There are two main types of signals: continuous-time signals defined over continuous variables like time, and discrete-time signals defined over discrete variables like time steps. Signals can be periodic if they repeat, or non-periodic. Any signal can be decomposed into even and odd components. The document also introduces the concepts of deterministic signals where values are fixed, versus random signals with uncertainty.
This document provides an introduction to signals and systems. It defines a signal as a function that carries information about a physical phenomenon, and a system as an entity that processes signals to produce new outputs. Signals can be classified as continuous or discrete, deterministic or random, periodic or aperiodic, even or odd, energy-based or power-based, and causal or noncausal. The document discusses examples and properties of different signal types and how systems manipulate inputs to generate outputs. It covers key concepts like energy, power, periodicity, causality, and system modeling that are important foundations for signals and systems analysis.
This document discusses pulse amplitude modulation (PAM) and matched filtering. It begins with an outline of topics to be covered, including PAM, matched filtering, PAM systems, intersymbol interference, and eye diagrams. It then provides definitions and illustrations of digital and analog PAM. The key aspects of matched filtering are introduced, including its use for pulse detection in additive noise. Derivations show that the optimal matched filter is a time-reversed and scaled version of the transmitted pulse shape. Intersymbol interference is discussed and methods to eliminate it are presented. Bit error probability calculations for binary PAM signals are also covered.
This document provides an overview of signal fundamentals, including definitions, examples, and properties of signals. It discusses topics such as signal energy and power, signal transformations, periodic and exponential signals. Examples are provided to illustrate concepts such as determining if a signal has finite energy/power, applying signal transformations, decomposing signals into even and odd components, and plotting exponential signals. The document is from a university course on signal fundamentals and is intended to introduce basic signal processing concepts.
This document discusses various operations that can be performed on signals. It was prepared by Dishant Patel, Vishal Gohel, Jay Panchal, and Manthan Panchal, and guided by Prof. Hardik Patel. The key operations discussed are time shifting, time scaling, time inversion/folding, amplitude scaling, addition, subtraction, and multiplication of signals. These basic operations are important for analyzing and manipulating signals for different purposes.
These notes were developed for use in the course Signals and Systems. The notes cover traditional, introductory concepts in the time domain and frequency domain analysis of signals and systems.
Es400 fall 2012_lecuture_2_transformation_of_continuous_time_signal.pptxumavijay
This document outlines transformations that can be applied to continuous-time signals, including time reversal, time scaling, time shifting, and amplitude transformations. It also discusses properties of even and odd signals. Time reversal flips the signal across the time axis. Time scaling stretches or compresses the time axis. Time shifting slides the signal along the time axis. Amplitude transformations multiply the signal by a constant and add an offset. The product of two even signals is even, while the product of an even and odd signal is odd.
This document provides an introduction to signals and systems. It begins by classifying different types of signals as continuous-time/discrete-time, analog/digital, deterministic/random, periodic/aperiodic, power/energy. It then discusses representations of signals in the time and frequency domains, including the Fourier series representation of periodic signals. Key concepts covered include the unit step, rectangular, triangular and sinc functions, as well as signal operations like time shifting, scaling and inversion. The document concludes by introducing Parseval's theorem relating the power of a signal to the power of its Fourier coefficients.
This document provides an overview of signals and systems. It defines signals as functions that carry information over time or discrete steps. There are two main types of signals: continuous-time signals defined over continuous variables like time, and discrete-time signals defined over discrete variables like time steps. Signals can be periodic if they repeat, or non-periodic. Any signal can be decomposed into even and odd components. The document also introduces the concepts of deterministic signals where values are fixed, versus random signals with uncertainty.
This document provides an introduction to signals and systems. It defines a signal as a function that carries information about a physical phenomenon, and a system as an entity that processes signals to produce new outputs. Signals can be classified as continuous or discrete, deterministic or random, periodic or aperiodic, even or odd, energy-based or power-based, and causal or noncausal. The document discusses examples and properties of different signal types and how systems manipulate inputs to generate outputs. It covers key concepts like energy, power, periodicity, causality, and system modeling that are important foundations for signals and systems analysis.
This document discusses pulse amplitude modulation (PAM) and matched filtering. It begins with an outline of topics to be covered, including PAM, matched filtering, PAM systems, intersymbol interference, and eye diagrams. It then provides definitions and illustrations of digital and analog PAM. The key aspects of matched filtering are introduced, including its use for pulse detection in additive noise. Derivations show that the optimal matched filter is a time-reversed and scaled version of the transmitted pulse shape. Intersymbol interference is discussed and methods to eliminate it are presented. Bit error probability calculations for binary PAM signals are also covered.
This document provides an overview of signal fundamentals, including definitions, examples, and properties of signals. It discusses topics such as signal energy and power, signal transformations, periodic and exponential signals. Examples are provided to illustrate concepts such as determining if a signal has finite energy/power, applying signal transformations, decomposing signals into even and odd components, and plotting exponential signals. The document is from a university course on signal fundamentals and is intended to introduce basic signal processing concepts.
This document discusses various operations that can be performed on signals. It was prepared by Dishant Patel, Vishal Gohel, Jay Panchal, and Manthan Panchal, and guided by Prof. Hardik Patel. The key operations discussed are time shifting, time scaling, time inversion/folding, amplitude scaling, addition, subtraction, and multiplication of signals. These basic operations are important for analyzing and manipulating signals for different purposes.
These notes were developed for use in the course Signals and Systems. The notes cover traditional, introductory concepts in the time domain and frequency domain analysis of signals and systems.
This document provides an introduction to signals and systems. It defines different types of signals including continuous-time and discrete-time signals. It describes important elementary signals like sinusoidal, exponential, unit step, unit impulse, and ramp functions. It discusses operations that can be performed on signals like time shifting, time scaling, and time inversion. It also classifies signals as deterministic vs non-deterministic, periodic vs aperiodic, even vs odd, and energy vs power signals. Key properties of different signal types are covered.
The document discusses various properties of signals including:
- Analog signals can have an infinite number of values while digital signals are limited to a set of values.
- Phase describes the position of a waveform relative to a reference point in time.
- Total energy and average power of continuous and discrete signals can be calculated through integrals and sums.
- Periodic, even, odd, exponential, and sinusoidal signals are described.
- Unit impulse and step signals are defined for both discrete and continuous time domains.
- A signal's frequency spectrum shows the collection of component frequencies and bandwidth is the range of these frequencies.
1. The document discusses operations that can be performed on continuous-time signals, including time reversal, time shifting, amplitude scaling, addition, multiplication, and time scaling.
2. It provides examples of each operation using the unit step function u(t) and illustrates the effect graphically. Combinations of operations are also demonstrated through examples.
3. Key operations include time shifting which delays a signal, time scaling which speeds up or slows down a signal, and their combination which first performs one operation and then the other.
The document provides information about a signals and systems course taught by Mr. Koay Fong Thai. It includes announcements about course policies, assessments, and schedule. Students are advised to ask questions, work hard, and submit assignments on time. The use of phones and laptops in class is strictly prohibited. The course aims to introduce signals and systems analysis using various transforms. Topics include signals in the time domain, Fourier transforms, Laplace transforms, and z-transforms. Reference books and a lecture schedule are also provided.
This document discusses concepts related to signals and systems. It begins by defining a signal as a time-varying quantity of information and a system as an entity that processes input signals to produce output signals. It then covers signal classification including continuous vs discrete time, analog vs digital, periodic vs aperiodic, deterministic vs random, and causal vs non-causal signals. Signal operations like time shifting, scaling, and inversion are described. Key concepts discussed in detail include signal size using energy and power, signal components and orthogonality, correlation as a measure of signal similarity, and trigonometric Fourier series. Worked examples are provided to illustrate various topics.
Instrumentation Engineering : Signals & systems, THE GATE ACADEMYklirantga
THE GATE ACADEMY's GATE Correspondence Materials consist of complete GATE syllabus in the form of booklets with theory, solved examples, model tests, formulae and questions in various levels of difficulty in all the topics of the syllabus. The material is designed in such a way that it has proven to be an ideal material in-terms of an accurate and efficient preparation for GATE.
Quick Refresher Guide : is especially developed for the students, for their quick revision of concepts preparing for GATE examination. Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions
GATE QUESTION BANK : is a topic-wise and subject wise collection of previous year GATE questions ( 2001 – 2013). Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions
Bangalore Head Office:
THE GATE ACADEMY
# 74, Keshava Krupa(Third floor), 30th Cross,
10th Main, Jayanagar 4th block, Bangalore- 560011
E-Mail: info@thegateacademy.com
Ph: 080-61766222
This document contains a question bank with two mark questions and answers related to signals and systems. Some key topics covered include:
- Definitions of continuous and discrete time signals like unit step, unit impulse, ramp functions.
- Classifications of signals as periodic, aperiodic, even, odd, energy and power.
- Properties of Fourier series and transforms including Dirichlet conditions, time shifting property, Parseval's theorem.
- Definitions of causal, non-causal, static and dynamic systems.
- Calculations of Fourier and Laplace transforms of basic signals like impulse, step functions.
So in summary, this document provides a review of fundamental concepts in signals and systems along with practice
The document discusses correlation functions and their use in designing optimal Wiener filters. It contains the following key points:
1. Correlation functions describe the relationships between input and output signals of a system and include the auto-correlation of the input, auto-correlation of the desired output, and cross-correlation between input and output.
2. The Wiener filter is a linear filter that minimizes the mean square error between the actual and desired filter output. It can be designed by determining the transfer function that results in the lowest mean square error based on the correlation functions.
3. For a stationary input signal, the optimal Wiener filter transfer function is derived by setting the cross-correlation between the input and
This document discusses various operations that can be performed on signals, including time shifting, time reversal, time scaling, signal addition, and signal multiplication. It provides examples and explanations of each operation. Time shifting involves shifting a signal along the time axis. Time reversal involves reversing a signal along the time axis. Time scaling involves compressing or expanding a signal along the time axis. Signal addition and multiplication involve combining two signals by adding or multiplying their corresponding sample values.
Signal and System, CT Signal DT Signal, Signal Processing(amplitude and time ...Waqas Afzal
Signal and System(definitions)
Continuous-Time Signal
Discrete-Time Signal
Signal Processing
Basic Elements of Signal Processing
Classification of Signals
Basic Signal Operations(amplitude and time scaling)
The finite time turnpike phenomenon for optimal control problemsMartinGugat
Often in dynamic optimal control problems with a long time horizon, in a large neighborhoodof the middle of the time interval the optimal control and the optimal state are very close to the solution of a static control problem that is derived form the dynamic optimal control problems by omitting the information about the initial state and possibly a desired terminal state.We show that for problems with a non-smooth tracking term in the objective function that is multiplied with a sufficiently large penalty-parameter in some cases the optimal state and the optimal controlreach the solution of the static control problem (the so-called turnpike) exactly after finite-time and remain there during a certain time-interval, until close to the end of the time interval possibly the state leaves the turnpike.This can be shown in different situations, for example under exact controllability assumptionsor with the assumption of nodal profile exact controllability, as studied byTatsien Li and his group.
Signals and Systems is an introduction to analog and digital signal processing, a topic that forms an integral part of engineering systems in many diverse areas, including seismic data processing, communications, speech processing, image processing, defense electronics, consumer electronics, and consumer products.
This document provides an overview of signals and systems. It defines key terms like signal, system, continuous and discrete time signals, analog and digital signals, periodic and aperiodic signals. It also discusses different types of signals like deterministic and probabilistic signals, energy and power signals. The document then classifies systems as linear/nonlinear, time-invariant/variant, causal/non-causal, and with/without memory. It provides examples of different signals and properties of signals like magnitude scaling, time shifting, reflection and scaling. Overall, the document introduces fundamental concepts in signals and systems.
1. The document discusses signals and systems, including continuous-time and discrete-time signals. It covers topics like transformations of signals, exponential and sinusoidal signals, and basic properties of systems.
2. Continuous-time signals are represented as functions of time t, while discrete-time signals are represented as sequences indexed by integer n. Exponential and sinusoidal signals can be represented using complex exponential functions.
3. The document provides examples and formulas for calculating energy, power, and other properties of signals. It also describes how signals can be transformed through operations like time shifting, scaling, reversal, and periodicity.
This document provides an introduction and syllabus for a signals and systems course taught by Prof. Satheesh Monikandan.B at the Indian Naval Academy. The syllabus covers topics such as signal classification, system properties, sampling, and transforms. It defines key concepts like signals, systems, continuous and discrete time signals, and linear and nonlinear systems. Elementary signals like sinusoidal, exponential, unit step, and impulse are also introduced.
EC8352- Signals and Systems - Unit 2 - Fourier transformNimithaSoman
This document discusses Fourier transforms and their applications. It begins by introducing Fourier transforms and noting that they are used widely in optics, image processing, speech processing, and medical signal processing. It then covers key topics such as:
- When periodic and aperiodic signals can be represented by Fourier series versus Fourier transforms
- Properties of continuous-time and discrete-time Fourier transforms
- Applications of Fourier transforms in filtering ECG signals, modeling diffractive gratings in optics, speech processing, and image processing
- Limitations of Fourier transforms in representing non-stable systems
The document provides an overview of Fourier transforms and their significance in decomposing signals into constituent frequencies, as well as examples of where they are applied in
This document outlines the course content for a Signals and Systems course. The following topics will be covered: continuous and discrete time linear time-invariant systems, the discrete Fourier transform, and the Z-transform. Chapter 1 introduces signals and their classification as analog or digital, deterministic or non-deterministic, periodic or aperiodic, even or odd, energy-based or power-based. Signal operations like time shifting, scaling, and inversion are also discussed. Sampling and quantization are explained with reference to the sampling theorem.
1) Signals can be classified as continuous-time or discrete-time based on their definition over time. Continuous-time signals are defined for every instant in time while discrete-time signals are defined at discrete time instances.
2) A system is defined as a set of elements or devices that produce an output in response to an input signal. The relationship between input and output signals is represented by a system operator.
3) Signals and systems can be further classified based on their properties, such as being deterministic or random, periodic or aperiodic, causal or non-causal, and more. Basic operations on signals include time scaling, time reversal, and time shifting.
This document provides an introduction to signals and systems. It begins by classifying different types of signals as continuous-time/discrete-time, analog/digital, deterministic/random, periodic/aperiodic, power/energy. It then discusses representations of signals in the time and frequency domains, including the Fourier series representation of periodic signals. Key concepts covered include the unit step, rectangular, triangular and sinc functions, as well as signal operations like time shifting, scaling and inversion. The document concludes by introducing Parseval's theorem relating the power of a signal to the power of its Fourier coefficients.
This document provides an introduction to signals and systems. It discusses various signal classifications including continuous-time vs discrete-time, and memory vs memoryless systems. Elementary signals such as unit step, impulse, and sinusoid functions are defined. Common signal operations including time reversal, time scaling, amplitude scaling and shifting are described. The relationships between the time and frequency domains are introduced. The document is intended to help students understand signal characteristics and operations in both the time and frequency domains.
Signals can be classified as continuous-time or discrete-time. Continuous-time signals have a value for all points in time, while discrete-time signals have values only at specific sample points. Common elementary signals include unit step, unit impulse, sinusoidal, and exponential functions. Signals can be further classified based on properties like periodicity, even/odd symmetry, and energy/power. Operations like time shifting, scaling, and inversion can be performed on signals. Discrete-time signals are often obtained by sampling continuous-time signals.
A signal is a pattern of variation that carry information.
Signals are represented mathematically as a function of one or more independent variable
basic concept of signals
types of signals
system concepts
This document provides an introduction to signals and systems. It defines different types of signals including continuous-time and discrete-time signals. It describes important elementary signals like sinusoidal, exponential, unit step, unit impulse, and ramp functions. It discusses operations that can be performed on signals like time shifting, time scaling, and time inversion. It also classifies signals as deterministic vs non-deterministic, periodic vs aperiodic, even vs odd, and energy vs power signals. Key properties of different signal types are covered.
The document discusses various properties of signals including:
- Analog signals can have an infinite number of values while digital signals are limited to a set of values.
- Phase describes the position of a waveform relative to a reference point in time.
- Total energy and average power of continuous and discrete signals can be calculated through integrals and sums.
- Periodic, even, odd, exponential, and sinusoidal signals are described.
- Unit impulse and step signals are defined for both discrete and continuous time domains.
- A signal's frequency spectrum shows the collection of component frequencies and bandwidth is the range of these frequencies.
1. The document discusses operations that can be performed on continuous-time signals, including time reversal, time shifting, amplitude scaling, addition, multiplication, and time scaling.
2. It provides examples of each operation using the unit step function u(t) and illustrates the effect graphically. Combinations of operations are also demonstrated through examples.
3. Key operations include time shifting which delays a signal, time scaling which speeds up or slows down a signal, and their combination which first performs one operation and then the other.
The document provides information about a signals and systems course taught by Mr. Koay Fong Thai. It includes announcements about course policies, assessments, and schedule. Students are advised to ask questions, work hard, and submit assignments on time. The use of phones and laptops in class is strictly prohibited. The course aims to introduce signals and systems analysis using various transforms. Topics include signals in the time domain, Fourier transforms, Laplace transforms, and z-transforms. Reference books and a lecture schedule are also provided.
This document discusses concepts related to signals and systems. It begins by defining a signal as a time-varying quantity of information and a system as an entity that processes input signals to produce output signals. It then covers signal classification including continuous vs discrete time, analog vs digital, periodic vs aperiodic, deterministic vs random, and causal vs non-causal signals. Signal operations like time shifting, scaling, and inversion are described. Key concepts discussed in detail include signal size using energy and power, signal components and orthogonality, correlation as a measure of signal similarity, and trigonometric Fourier series. Worked examples are provided to illustrate various topics.
Instrumentation Engineering : Signals & systems, THE GATE ACADEMYklirantga
THE GATE ACADEMY's GATE Correspondence Materials consist of complete GATE syllabus in the form of booklets with theory, solved examples, model tests, formulae and questions in various levels of difficulty in all the topics of the syllabus. The material is designed in such a way that it has proven to be an ideal material in-terms of an accurate and efficient preparation for GATE.
Quick Refresher Guide : is especially developed for the students, for their quick revision of concepts preparing for GATE examination. Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions
GATE QUESTION BANK : is a topic-wise and subject wise collection of previous year GATE questions ( 2001 – 2013). Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions
Bangalore Head Office:
THE GATE ACADEMY
# 74, Keshava Krupa(Third floor), 30th Cross,
10th Main, Jayanagar 4th block, Bangalore- 560011
E-Mail: info@thegateacademy.com
Ph: 080-61766222
This document contains a question bank with two mark questions and answers related to signals and systems. Some key topics covered include:
- Definitions of continuous and discrete time signals like unit step, unit impulse, ramp functions.
- Classifications of signals as periodic, aperiodic, even, odd, energy and power.
- Properties of Fourier series and transforms including Dirichlet conditions, time shifting property, Parseval's theorem.
- Definitions of causal, non-causal, static and dynamic systems.
- Calculations of Fourier and Laplace transforms of basic signals like impulse, step functions.
So in summary, this document provides a review of fundamental concepts in signals and systems along with practice
The document discusses correlation functions and their use in designing optimal Wiener filters. It contains the following key points:
1. Correlation functions describe the relationships between input and output signals of a system and include the auto-correlation of the input, auto-correlation of the desired output, and cross-correlation between input and output.
2. The Wiener filter is a linear filter that minimizes the mean square error between the actual and desired filter output. It can be designed by determining the transfer function that results in the lowest mean square error based on the correlation functions.
3. For a stationary input signal, the optimal Wiener filter transfer function is derived by setting the cross-correlation between the input and
This document discusses various operations that can be performed on signals, including time shifting, time reversal, time scaling, signal addition, and signal multiplication. It provides examples and explanations of each operation. Time shifting involves shifting a signal along the time axis. Time reversal involves reversing a signal along the time axis. Time scaling involves compressing or expanding a signal along the time axis. Signal addition and multiplication involve combining two signals by adding or multiplying their corresponding sample values.
Signal and System, CT Signal DT Signal, Signal Processing(amplitude and time ...Waqas Afzal
Signal and System(definitions)
Continuous-Time Signal
Discrete-Time Signal
Signal Processing
Basic Elements of Signal Processing
Classification of Signals
Basic Signal Operations(amplitude and time scaling)
The finite time turnpike phenomenon for optimal control problemsMartinGugat
Often in dynamic optimal control problems with a long time horizon, in a large neighborhoodof the middle of the time interval the optimal control and the optimal state are very close to the solution of a static control problem that is derived form the dynamic optimal control problems by omitting the information about the initial state and possibly a desired terminal state.We show that for problems with a non-smooth tracking term in the objective function that is multiplied with a sufficiently large penalty-parameter in some cases the optimal state and the optimal controlreach the solution of the static control problem (the so-called turnpike) exactly after finite-time and remain there during a certain time-interval, until close to the end of the time interval possibly the state leaves the turnpike.This can be shown in different situations, for example under exact controllability assumptionsor with the assumption of nodal profile exact controllability, as studied byTatsien Li and his group.
Signals and Systems is an introduction to analog and digital signal processing, a topic that forms an integral part of engineering systems in many diverse areas, including seismic data processing, communications, speech processing, image processing, defense electronics, consumer electronics, and consumer products.
This document provides an overview of signals and systems. It defines key terms like signal, system, continuous and discrete time signals, analog and digital signals, periodic and aperiodic signals. It also discusses different types of signals like deterministic and probabilistic signals, energy and power signals. The document then classifies systems as linear/nonlinear, time-invariant/variant, causal/non-causal, and with/without memory. It provides examples of different signals and properties of signals like magnitude scaling, time shifting, reflection and scaling. Overall, the document introduces fundamental concepts in signals and systems.
1. The document discusses signals and systems, including continuous-time and discrete-time signals. It covers topics like transformations of signals, exponential and sinusoidal signals, and basic properties of systems.
2. Continuous-time signals are represented as functions of time t, while discrete-time signals are represented as sequences indexed by integer n. Exponential and sinusoidal signals can be represented using complex exponential functions.
3. The document provides examples and formulas for calculating energy, power, and other properties of signals. It also describes how signals can be transformed through operations like time shifting, scaling, reversal, and periodicity.
This document provides an introduction and syllabus for a signals and systems course taught by Prof. Satheesh Monikandan.B at the Indian Naval Academy. The syllabus covers topics such as signal classification, system properties, sampling, and transforms. It defines key concepts like signals, systems, continuous and discrete time signals, and linear and nonlinear systems. Elementary signals like sinusoidal, exponential, unit step, and impulse are also introduced.
EC8352- Signals and Systems - Unit 2 - Fourier transformNimithaSoman
This document discusses Fourier transforms and their applications. It begins by introducing Fourier transforms and noting that they are used widely in optics, image processing, speech processing, and medical signal processing. It then covers key topics such as:
- When periodic and aperiodic signals can be represented by Fourier series versus Fourier transforms
- Properties of continuous-time and discrete-time Fourier transforms
- Applications of Fourier transforms in filtering ECG signals, modeling diffractive gratings in optics, speech processing, and image processing
- Limitations of Fourier transforms in representing non-stable systems
The document provides an overview of Fourier transforms and their significance in decomposing signals into constituent frequencies, as well as examples of where they are applied in
This document outlines the course content for a Signals and Systems course. The following topics will be covered: continuous and discrete time linear time-invariant systems, the discrete Fourier transform, and the Z-transform. Chapter 1 introduces signals and their classification as analog or digital, deterministic or non-deterministic, periodic or aperiodic, even or odd, energy-based or power-based. Signal operations like time shifting, scaling, and inversion are also discussed. Sampling and quantization are explained with reference to the sampling theorem.
1) Signals can be classified as continuous-time or discrete-time based on their definition over time. Continuous-time signals are defined for every instant in time while discrete-time signals are defined at discrete time instances.
2) A system is defined as a set of elements or devices that produce an output in response to an input signal. The relationship between input and output signals is represented by a system operator.
3) Signals and systems can be further classified based on their properties, such as being deterministic or random, periodic or aperiodic, causal or non-causal, and more. Basic operations on signals include time scaling, time reversal, and time shifting.
This document provides an introduction to signals and systems. It begins by classifying different types of signals as continuous-time/discrete-time, analog/digital, deterministic/random, periodic/aperiodic, power/energy. It then discusses representations of signals in the time and frequency domains, including the Fourier series representation of periodic signals. Key concepts covered include the unit step, rectangular, triangular and sinc functions, as well as signal operations like time shifting, scaling and inversion. The document concludes by introducing Parseval's theorem relating the power of a signal to the power of its Fourier coefficients.
This document provides an introduction to signals and systems. It discusses various signal classifications including continuous-time vs discrete-time, and memory vs memoryless systems. Elementary signals such as unit step, impulse, and sinusoid functions are defined. Common signal operations including time reversal, time scaling, amplitude scaling and shifting are described. The relationships between the time and frequency domains are introduced. The document is intended to help students understand signal characteristics and operations in both the time and frequency domains.
Signals can be classified as continuous-time or discrete-time. Continuous-time signals have a value for all points in time, while discrete-time signals have values only at specific sample points. Common elementary signals include unit step, unit impulse, sinusoidal, and exponential functions. Signals can be further classified based on properties like periodicity, even/odd symmetry, and energy/power. Operations like time shifting, scaling, and inversion can be performed on signals. Discrete-time signals are often obtained by sampling continuous-time signals.
A signal is a pattern of variation that carry information.
Signals are represented mathematically as a function of one or more independent variable
basic concept of signals
types of signals
system concepts
1. The document discusses Fourier analysis techniques for representing signals, including Fourier series and the Fourier transform. It uses the example of a rectangular pulse train to illustrate these concepts.
2. A periodic signal like a rectangular pulse train can be represented by a Fourier series as a sum of sinusoids with frequencies that are integer multiples of the fundamental frequency.
3. The Fourier transform allows representing aperiodic signals as a sum of sinusoids of all possible frequencies, resulting in a continuous spectrum rather than a discrete line spectrum. The Fourier transform of a rectangular pulse is a sinc function.
1) Signals can be classified as continuous-time or discrete-time based on how they are defined over time. Continuous-time signals are defined for every instant in time while discrete-time signals are defined at discrete time instances.
2) A system is defined as a set of elements or devices that produce an output response to an input signal. The relationship between input and output signals is represented by a system operator.
3) Signals and systems can be further classified based on their properties, such as being deterministic or random, periodic or aperiodic, causal or non-causal, and more. Basic operations on signals include time scaling, time reversal, and time shifting.
1) Pulse amplitude modulation (PAM) encodes digital information by varying the amplitude of a periodic pulse train based on a sampled message signal. 2) A matched filter is used at the receiver to detect pulses in the presence of noise. The matched filter is a time-reversed and scaled version of the transmitted pulse shape. 3) Intersymbol interference can occur when pulses are transmitted too closely together. Adding a guard period between pulses or using a raised cosine pulse shape can eliminate intersymbol interference.
This document provides an overview of signals and systems. It defines key terms like signals, systems, continuous and discrete time signals, analog and digital signals, deterministic and probabilistic signals, even and odd signals, energy and power signals, periodic and aperiodic signals. It also classifies systems as linear/non-linear, time-invariant/variant, causal/non-causal, and with or without memory. Singularity functions like unit step, unit ramp and unit impulse are introduced. Properties of signals like magnitude scaling, time reflection, time scaling and time shifting are discussed. Energy and power of signals are defined.
This document provides an overview of signals and systems. It defines a signal as a physical quantity that varies with time and contains information. Signals are classified as deterministic or non-deterministic, periodic or aperiodic, even or odd, energy-based or power-based, and continuous-time or discrete-time. Systems are combinations of elements that process input signals to produce output signals. Key properties of systems include causality, linearity, time-invariance, stability, and invertibility. Applications of signals and systems are found in control systems, communications, signal processing, and more.
Signals and Systems-Fourier Series and TransformPraveen430329
This document discusses analysis of continuous time signals. It begins by introducing Fourier series representation of periodic signals using trigonometric and exponential forms. It describes properties of Fourier series such as linearity, time shifting, and frequency scaling. It then introduces the Fourier transform which transforms signals from the time domain to the frequency domain. Common Fourier transform pairs are listed. The Laplace transform is also introduced which transforms signals from the time domain to the complex s-domain. Key properties of the Laplace transform include linearity, scaling, time shifting, and the initial and final value theorems. Conditions for the existence of the Laplace transform are also provided.
1. The document discusses operations that can be performed on continuous-time signals, including time reversal, time shifting, amplitude scaling, addition, multiplication, and time scaling.
2. It provides examples of each operation using the unit step function u(t) and illustrates the effect graphically. Combinations of operations are also demonstrated through examples.
3. Key operations include time shifting which delays a signal, time scaling which speeds up or slows down a signal, and their combination which first performs one operation and then the other.
The document discusses frequency modulation techniques, specifically GMSK modulation. It provides an overview of digital modulation, describes the key parameters and expression for GMSK modulation, and discusses implementing a GMSK modulator. It explains that GMSK modulation uses continuous phase modulation with a Gaussian frequency shaping filter. The document also provides the mathematical expressions for the GMSK modulated signal and describes calculating the baseband components and elementary phase pulse using Matlab.
Introduction to communication system part 2Unit-I Part 2.pptxAshishChandrakar12
This document contains information about a course on communication systems including:
1) The course contains 5 units covering topics like introduction to communication systems, amplitude modulation, angle modulation, transmitters and receivers, and noise in analog communication.
2) Textbook references are provided for each unit from authors like Taub and Schilling, George F Kennedy, Simon Haykin, and R P Singh.
3) Additional reference books are also listed including works by Proakis and B.P. Lathi.
4) Unit 1 is further described covering topics like classification of signals, Fourier transforms, signal bandwidth, distortionless transmission, Parseval's theorem, and introduction to convolution and correlation of signals.
5
Introduction of communication system_Unit-I Part 2.pptxAshishChandrakar12
This document discusses various types of signals that are commonly used in communication systems. It covers topics such as:
1) Signals can be classified based on properties like continuity, amplitude quantization, periodicity, causality, symmetry, and length. Common types include continuous-time/discrete-time, analog/digital, periodic/aperiodic, causal/non-causal, even/odd, and finite/infinite length signals.
2) Operations like time-shifting, scaling, and inversion are useful for analyzing and manipulating signals.
3) Key concepts for characterizing signal strength include energy, power, and norms. Energy signals have finite energy while power signals have finite non-zero power
Unit 1 -Introduction to signals and standard signalsDr.SHANTHI K.G
1) The document introduces various types of signals including continuous time signals, discrete time signals, standard signals like step signals, ramp signals, impulse signals, sinusoidal signals, and exponential signals.
2) Continuous time signals are defined for every instant in time while discrete time signals are defined for discrete instants in time. Common standard signals include unit step, ramp, parabolic, pulse, sinusoidal, and exponential signals.
3) Examples of applications of the standard signals are mentioned such as step signals being used for switching devices on and off, and sinusoidal signals being used to represent any sound signal.
The document discusses frequency domain processing and the Fourier transform. It defines key concepts such as:
- The frequency domain represents how much of a signal lies within different frequency bands, while the time domain shows how a signal changes over time.
- The Fourier transform provides the frequency domain representation of a signal and is used to analyze signals with respect to frequency. Its inverse transform reconstructs the original signal.
- The Fourier transform decomposes a signal into orthogonal sine and cosine waves of different frequencies, showing the contribution of each frequency component. This representation is important for signal processing tasks like filtering.
1. The document discusses analog to digital conversion (ADC) and digital to analog conversion (DAC). It explains that ADC involves sampling an analog signal and encoding it into a discrete-time, discrete-amplitude digital signal. DAC uses a zero-order hold to keep the output fixed at the latest digital value until the next sample time.
2. The document derives the transfer function of a zero-order hold, which is used in DAC. It shows that a zero-order hold can be represented by the equation m(t) = u(t) - u(t-T), where T is the sampling period.
3. The document notes that digital systems offer advantages over analog systems like accuracy
This document provides an overview of chapter 1 on signals from a textbook on signals and systems. It defines a signal as a function that varies over time or another independent variable. It classifies signals as continuous-time or discrete-time, even or odd, periodic or aperiodic, and energy or power signals. It also discusses transformations of signals including time shifting, time scaling, and time reversal. Exponential and sinusoidal signals are examined for both continuous-time and discrete-time cases. Finally, it introduces the unit impulse and unit step functions.
1. The document provides a list of 2 mark questions and answers related to the Signals and Systems subject for the 3rd semester IT students.
2. It includes definitions of key terms like signal, system, different types of signals and their classifications. Properties of Fourier series and Fourier transforms are also covered.
3. The questions address topics ranging from periodic/aperiodic signals, even/odd signals, unit step and impulse functions, Fourier series, Fourier transforms, Laplace transforms, linear and time invariant systems.
This document discusses sampling and related concepts in signal processing. It begins by introducing the need to convert analog signals to discrete-time signals for digital processing. It then covers the sampling theorem, which states that a band-limited signal can be reconstructed if sampled at twice the maximum frequency. The document describes three main sampling methods: ideal (impulse), natural (pulse), and flat-top sampling. It also discusses aliasing, which occurs when a signal is under-sampled. The key aspects of sampling covered are the sampling rate, reconstruction of sampled signals, and anti-aliasing filters.
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Eeb317 principles of telecoms 2015
1. Principles of Telecommunications
• Communication is the largest sector of the
electronics field, hence knowledge &
understanding is a must for every student
• The field of Electronic Communication changes
so fast
• Need for Firm Grounding in Fundamentals: also
understanding of the real world components,
circuits, equipment & systems in everyday use.
• Balance in Principles of latest techniques
• Study the system level understanding
2. EEB317 Principles of Telecoms
•Signals & Systems
•Amplitude Modulation
•Angle Modulation
•Detection & Demodulation
•Noise in Communications System
4. Overview
• Tx of information between 2 distant points
• Dominated by 4 important sources: speech,
television, facsimile & personal computers
• Three basic processes:
• Transmitter, Channel & Receiver
8. Classification of signals & Systems
• A system is an interacting set of physical
objects or physical conditions called system
components
• A signal: set of information or data. Can be
input, output or internal
• Signals may be functions of independent
variables such as time, distance, force, position,
pressure, temp … for simplicity only time will be
used in this class
9. • Mathematical models are mathematical
equations that represent signals & systems
• They permit quantitative analysis and design of
signals & systems
• Continuous-time signal x(t), has a value
specified for all points in time, & a continuous-
time system operates on and produces
continuous-time signals
12. Signals
• Discrete-time signal: Signal specified only at
discrete values
• Analog signal: Signal whose amplitude can
take on any value in a continuous range
• Digital signal: Signal whose amplitude can
take on only finite number of values (M-ary)
• Periodic signal: Signal g(t) is periodic if for
some +ve constant T0 (period):
)()( 0Ttgtg
14. Energy & Power Signals
• Energy signal: Signal with finite energy & zero
power
• Power signal: Signal with finite power & infinite
energy
dttgE
2
)(
2/
2/
2
2/
2/
2
)(
1
lim
)(
1
lim00
T
TT
T
TT
dttg
T
P
dttg
T
P
16. Energy & Power Signals examples
• Since in (a) amplitude approaches zero
• It’s an energy signal:
• Since (b) is periodic, it’s a power signal:
t
84422)(
0
20
1
22 2/
dtedtdttgE
t
3
1
3
2
1
)(
1
)(
1
lim
32
1
1
1
1
1
21
1
22/
2/
2
t
dttdttg
T
dttg
T
P
T
TT
17. Worked example
• Determine the power of the following signals
)cos()( tCtg
2/
2/
22
2/
2/
22
2/
2/
22/
2/
2
2
)]22cos(1[
2
)(cos
1
)cos(
1
)(
1
lim
T
T
T
T
T
T
T
TT
C
dtt
T
C
P
dttC
T
dttC
T
dttg
T
P
18. Work these out
• (b)
• (c)
)cos()cos()( 222111 tCtCtg
21
tj
Detg 0
)(
19. More examples
• Compute the signal energy & signal power for
the following complex valued signal and
indicate whether the signal is an energy or
power signal
tj
Aetg 2
)(
20. More examples
• Since g(t) is a periodic signal, it cannot be an
energy signal. Therefore compute the signal
power first. Signal Period:
• Since the signal has a finite power, it is a power
signal & has infinite energy (VERIFY!)
1
0 T
2/122
2
2 1
1
/11
1
/11
1
AtAdtAdtAeP
t
t
tj
t
t
t
t
21. Deterministic & Random Signals
• Deterministic signal: Physical description is
known in either a mathematical or graphical
form. eg:
• Random signal: Signal known only in terms of
probabilistic description such as mean value,
mean square value rather than its complete
mathematical or graphical description
• eg: noise signal, message signal
)1(tan)( 1
ttg
22. Deterministic & Random Signals
• Use matlab to plot a deterministic signal:
• & random noise
• To use matlab you must:
• (a) declare the variables
• (b) since it’s first time, use the plot command
• (c) label the plot
)1(tan)( 1
ttg
23. Signal Operations
• Time shifting: If a signal g(t) is time shifted by
t1 units, it is denoted as f(t) =g(t-t1).
• If t1>0, the shift is to the right (time delay)
• If t1<0, the shift is to the left (time advance)
• To demonstrate time shifting plot the signals:
)1(tan)(
)1(tan)(
)(tan)(
1
1
1
ttY
ttG
ttg
24. Time Shift matlab code
• close all; % close graghs
• clear all; % clear all the variables & functions from memory
• t = -5:.3:5; % declear variable "t"
• g = atan(t);
• G = atan(t-1);
• Y = atan(t+1);
• plot(t,g); % plots the function "g"
• hold;
• plot(t,G,'r'); % plots “G”
• plot(t,Y,'k');
• hold off;
• grid on;
• xlabel('t');
• ylabel('g(t),G(t) & Y(t)');
• title('time shifting demonstration');
• legend('g-original','G-delay','Y-advance');
26. Signal Operations
• Time Scaling: Compression or expansion of a
signal
• Signal f(t) is g(t) compressed by a factor of ‘a’ if
f(t) = g(at), therefore f(t/a) = g(t) for a>1
• Similarly f(t) is g(t) expanded (slowed down) by
a factor of ‘a’ if f(t) = g(t/a), therefore f(at) = g(t)
for a<1
• To time-scale a signal by a factor of ‘a’, replace
t with at.
• If a > 1 the scaling is compressed & if a < 1,
the scaling is expanded.
27. Time Scaling demonstration
• close all;
• clear all;
• t = -5:.3:5;
• f = sawtooth(t);
• G = sawtooth(2*t);
• F = sawtooth(t/2);
• plot(t,f); hold;
• plot(t,G,'r');
• grid on;
• xlabel('t');
• ylabel('f(t) & G(t)');
• title('time scaling demonstration');
• legend('f','G');
29. Signal Operations
• Time Reversal/Inversion/Folding:
• To time reverse a signal, replace t with –t
• If f(t) is a time resersal of g(t) then
• f(t)=g(-t)
• See the matlab code of g(-t)
30. Time Reversal Demo-code
• close all; clear all;
• t = -5:.3:5;
• g = atan(t);
• G = atan(-t);
• plot(t,g); % hold;
• plot(t,G,'r'); % hold off;
• grid on;
• xlabel('t');
• ylabel('g(t) & G(t)');
• title('time Reversal Demonstration');
• legend('f-original', 'G-timeReversed');
31.
32. • Continous time signal: g(t)
• Samples of continuous-time signal: g(nT)
• Discrete-time signal: g(n)
33. Samples of Continuous-time signal
• close all; clear all;
• t=-5:.5:5;
• g=atan(t);
• plot(t,g);
• ylabel('g(t)');
• grid on;
• title('Continuous-time signal Demonstration');
• figure
• stem(t,g);
• grid on;
• xlabel('nT');
• ylabel('g(nT)');
• title('Samples of Continuous-time signal');
34.
35. Delta Function
• Delta/Dirac/Unit Impulse function:
Rectangular pulse with an infinitesimally small
width & infinitely large height & an overall area
of unity.
1)(
0)(
dtt
t
0t
37. Sampling/sifting property
• The area under the product of a function with
delta is equal to the value of that function at the
instant where delta is located
• Function f(t) must be continuous where the
delta is located
38. Unit Step Function
t
d
1
0
)( 0
0
t
t
t
tud )()(
)(t
dt
du
39. Time Shifted, scaled, reversed step
• Causal function: It’s zero before t = 0 otherwise
is non-causal
)(
)(
)(
a
b
tu
a
b
tu
batu
0
0
t
t
41. Fourier Series
• Fourier analysis considers signals to be
constructed from a sum of complex
exponentials with appropriate frequencies,
amplitude & phases
• Frequency components are the complex
exponentials (sines & cosines) which, when
added together, make up the signal
• Orthogonality of signal set: ntxtxtx )(),...(),( 21
43. Exponential FS
• Orthogonality:
• Expon. FS
0
)( 0
)(
0
00
0
0
T
dtedtee
T
tnmjtjn
T
tjm
nm
nm
0
0
0
)(
1
)(
0
T
tjn
n
n
tjn
n
dtetg
T
D
eDtg
44. Parseval’s Theorem
• Energy of the sum of orthogonal signals is
equal to the sum of their energies:
• Parseval’s theorem:
1
2
1
2
1
2
1
2
1
2
1
222
111
2
1
2
1
)()(
)....()(
);()(
EcdttxcdttxcE
txctg
txctg
t
t
t
t
1g
n
n
ng
g
EcE
EcEcE
2
2
2
21
2
1 ...
45. Trigonometric Fourier Series
• Trig. FS
01
1
01
1
01
1
01
1
01
1
0
0
0
0
0
0
0
2
0
0
1
00
2sin)(
2
)(
1
2cos)(
2
2cos
2cos)(
2sin2cosag(t)
Tt
t
n
Tt
t
Tt
tTt
t
Tt
t
n
n
n
n
tdtfntg
T
b
dttg
T
a
tdtfntg
Ttdtfn
tdtfntg
a
tfnbtfna
46. Fourier Transform & Spectra of
Aperiodic Signals
• The spectrum of a periodic signal is found from
FS of a signal over one period
• Since the FS is a periodic function of time, it is
equal to an aperiodic signal only over the FS
expansion interval, outside this interval it
repeats
• FS is used to produce the spectrum of the
periodic extension but not the spectrum of
aperiodic signal
• To find the spectrum of an aperiodic signal we
use FT
47. Fourier Transform (FT)
• To develop the FT, let’s start with the exponential FS
representation of a periodic signal over the interval
-T/2<t<T/2
• Let the interval increase until the entire time axis is
encompassed
• Since FT is developed from the FS the conditions for
the existence follow from those of the Dirichlet
conditions
dttg )(
50. Fourier Transform Theorems
• FT characteristics are expressed in the form of
theorems
• The theorems are useful in computing FT of
complicated signals
• Linearity:
• If x(t) X(f) & y(t) Y(f)
• Then
• ax(t)+by(t) aX(f)+bY(f)
• Integral in a linear operation