Signal & system
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This document defines and provides examples of various types of signals and systems. It discusses continuous and discrete time signals, even and odd signals, deterministic and random signals, periodic and aperiodic signals. It also defines linear and nonlinear systems, time invariant systems, causal and non-causal systems, memory and memoryless systems, and stable and unstable systems. Examples are provided for each type of signal and system defined.
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A harmonic wave is traveling on a string at 0.25 m/s. The displacement of the string at x = 0.015 m varies with time according to the equation D(0.015, t) = (0.09 m) sin (1.5 – 2.5t). The frequency is calculated to be 0.4 Hz, the wavelength is 0.63 m, and the phase constant is 1.4 rad. The general equation for the wave is determined to be D(x, t) = 0.09sin[2π/0.63 (x) – 2.5t + 1.4].
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A harmonic wave is traveling on a string at 0.25 m/s. The displacement of the string at x = 0.015 m varies with time according to the equation D(0.015, t) = (0.09 m) sin (1.5 – 2.5t). The frequency is calculated to be 0.4 Hz, the wavelength is 0.63 m, and the phase constant is 1.4 rad. The general equation for the wave is determined to be D(x, t) = 0.09sin[2π/0.63 (x) – 2.5t + 1.4].
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2. Key properties and theorems of the Laplace transform are described, including its use in solving linear time-invariant differential equations by taking the Laplace transform of both sides of the equation.
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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.
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- Prior to Fourier's work, there was no known solution to the heat equation in the general case. Fourier's idea was to model a complicated heat source as a superposition of simple sine and cosine waves.
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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.
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- Transform pairs for common functions like unit step, unit impulse, exponentials, sinusoids
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This document discusses periodic functions and Fourier series. A periodic function repeats its values over regular intervals called periods. The Fourier series represents periodic functions as the sum of trigonometric functions (sines and cosines) with different frequencies. The document derives the formulas to calculate the coefficients of the Fourier series from a given periodic function. It involves integrating the function multiplied by sines and cosines over one period of the function.
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This document discusses frequency concepts in continuous and discrete time signals. For continuous time signals, frequency is defined as cycles per second and relates to the periodic nature of sinusoidal signals. Discrete time signals are periodic only if the frequency is a rational number. The fundamental period is the smallest value that makes the signal periodic. As frequency increases for both continuous and discrete signals, the number of oscillations increases but the period decreases.
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This document discusses different types of signals. It defines a signal as a function that conveys information about a physical phenomenon. Signals can be one-dimensional or multi-dimensional depending on the number of variables. Both continuous and discrete signals are further classified as deterministic or random, periodic or non-periodic, energy or power signals, causal or non-causal, and even or odd. Deterministic signals have predictable behavior while random signals do not. Periodic signals repeat after a time period versus non-periodic signals. Energy signals have finite energy and zero power, while power signals have infinite energy. Causal signals are zero for negative time indexes and non-causal signals exist for both positive and negative time.
Signals & systems
This document contains lecture notes on signals and systems for a course at Chadalawada Ramanamma Engineering College. It includes:
1. An introduction to signals, systems, and some common elementary signals like the unit step, unit impulse, ramp, sinusoid, and exponential signals.
2. A classification of signals as continuous/discrete, deterministic/non-deterministic, even/odd, periodic/aperiodic, energy/power, and real/imaginary.
3. A discussion of basic operations on signals like amplitude scaling, addition, and subtraction.
Unit 8
This document provides an overview of continuous-time and discrete-time signals. It discusses representing continuous signals using complex exponentials and the concept of periodicity. When a continuous signal is sampled, it results in a discrete-time signal. The z-transform is introduced as a method to analyze discrete sequences. The document outlines various properties of z-transforms and regions of convergence. It also discusses inverse z-transforms using partial fractions and power series expansions.
Types of signals/functions & Difference b/w Fourier and Laplace transform
This document discusses various types of signals that can be analyzed using mathematical methods of physics. It defines signals and differentiates between continuous and discrete signals. It also describes deterministic and random signals, periodic and non-periodic signals, causal and non-causal signals, and energy and power signals. The document explains the Fourier transform and Laplace transform as mathematical tools to convert signals between the time and frequency domains. It notes some key differences between the Fourier and Laplace transforms, such as the Fourier transform being a special case of the two-sided Laplace transform.
Lecture 1 (ADSP).pptx
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.
Signals and System
This document contains the course syllabus for the Signals and Systems course at Karpagam Institute of Technology. It covers five units: (1) classification of signals and systems, (2) analysis of continuous time signals, (3) linear time invariant continuous time systems, (4) analysis of discrete time signals, and (5) linear time invariant discrete time systems. The first unit defines common signals like step, ramp, impulse, and sinusoidal signals and classifies signals and systems. It also introduces concepts of continuous and discrete time signals, periodic and aperiodic signals, and deterministic and random signals.
Signals and System
This document discusses digital signal processing and defines key concepts related to signals and systems. It defines a signal as a function of one or more variables that conveys information, and can be one-dimensional or multi-dimensional. Signals are classified as deterministic or random, natural or artificial, continuous or discrete, periodic or non-periodic, causal or non-causal, even or odd, energy-based or power-based. Systems are combinations of elements that process input signals to produce output signals. Systems are classified as static or dynamic, time-invariant or time-variant, linear or non-linear, causal or non-causal, stable or unstable. The document also discusses common operations that can be performed on signals like addition
signal and system Lecture 1
This document provides an introduction to signals and systems. It defines signals as functions that represent information over time and gives examples such as sound waves and stock prices. Systems are defined as generators or transformers of signals. Signal processing involves manipulating signals to extract useful information, often by converting them to electrical forms. The document then classifies different types of signals such as continuous-time vs discrete-time, analog vs digital, deterministic vs random, and energy vs power signals. It also introduces some basic continuous-time signals like the unit step function, unit impulse function, and complex exponential signals.
Signals and Systems.pptx
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.
Signals and Systems.pptx
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.
s and s ppt.pptx
This document provides an overview of a course on signals and systems. It outlines the course outcomes which include explaining various signal and system types using Fourier series and transforms. It also describes analyzing signals through linear systems. The syllabus covers topics like Fourier series, continuous and discrete time Fourier transforms, Laplace and z-transforms, and signal transmission through linear systems. Basic signal types and signal classification are defined. Operations on signals like amplitude scaling and addition are also introduced.
Sampling theorem
The document discusses sampling theory and analog-to-digital conversion. It begins by explaining that most real-world signals are analog but must be converted to digital for processing. There are three steps: sampling, quantization, and coding. Sampling converts a continuous-time signal to a discrete-time signal by taking samples at regular intervals. The sampling theorem states that the sampling frequency must be at least twice the highest frequency of the sampled signal to avoid aliasing. Finally, it provides an example showing how to calculate the minimum sampling rate, or Nyquist rate, given the highest frequency of a signal.
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Signal & system
- 3. Moazzam Arshad 2016-Uet-Qet.Swl-Elect-06 Sohail Ahmad 2016-Uet-Qet.Swl-Elect-08 Zain Zaeem 2016-Uet-Qet.Swl-Elect-02 Farooq Ahmad 2016-Uet-Qet.Swl-Elect-05
- 4. The signals are detectable physical quantities that vary with time, space or any other independent variable or variables. For Example: Sine Wave
- 5. Signals can be classified as: Continuous time Signals Discrete time Signals
- 6. If the independent variable (t) is continuous, then the corresponding signal is continuous time signal. For Example:
- 7. If the independent variable (t) takes on only discrete values. For Example:
- 8. Even and Odd Signals Energy and Power Signals Deterministic and Random Signal Periodic and APeriodic Signals
- 9. If by changing independent axis, without changing dependent axis the magnitude of the signal remains same, the signal is termed as even signal. For Example: Cosine Signal f (t) = f (-t) f(x)= x^2 All Square roots is Even Signal
- 10. When independent variable is changed and there is significant change in the amplitude of function, it is called odd signal. For Example: Sine Signal. f (t) =- f (-t) f(x) = x
- 11. Any signal squared and integrated over time where it exists is energy signal. Theses signals contain finite amount of energy and zero power. Time average of energy signal is Power signal, they contain infinite energy.
- 12. A random signal cannot be described by any mathematical function. For Example:
- 13. Deterministic Signal is one that can be described mathematically. For Example:
- 14. Any continuous-time signal that satisfies the condition: x(t+T) is a periodic Signal. m1T1=m2T2 = Tₒ = Fundamental period For Example: cos(tp/3)+sin(tp/4) T1=(2p)/(p/3)=6; T2 =(2p)/(p/4)=8; T1/T2=6/8 = (rational number) = m2/m1 m1T1=m2T2 >Find m1 and m2 6.4 = 3.8 = 24 = Tₒ
- 15. APeriodic Signals is not satisfy Equation. For Example: x(t) = u(t) - ½ x(t) = 4u(t) + 2sin(3t) x(t) = cos(4t) + 2sin(8t) x(t) = 3cos(4t) + sin(pt) x(t) = cos(3pt) + 2cos(4pt)
- 16. A set of principles or procedures according to which something is done. An organized scheme or method. For Example: Robot Arm and Remote TV
- 17. Systems can be classified as: Linear and Non linear Systems Time Invariant Systems Causal and Non- Causal Systems Memory and Memory less Systems Stable and Unstable Systems
- 18. A system which depends upon past and future values is called a Memory System. For Example: y(t) = 3x(t) + 4x(t+6) y(t) = 2x(t) + x(t-4) y(t) = 4x(t) + 3x(t+6)
- 19. A system is said to be memory less, if their present value of the output depends only on the present value of the input. For Example: y(t) = x(t) Y(t) = 3x(t)
- 20. System which outputs are dependent on present and past input, system is called causal system. For Example: y(t) = 3x(t) + x(t-2) y(t) = 5x(t) + 3x(t+5) y(t) = 3x(t)
- 21. Non causal systems are those systems, the output of which depends on future inputs. For Example: y(t) = 5x(t) + 3x(t+5) y(t) = 2x(t) + 3x(t- 4)+4x(t+6) y(t) = 4x(t+3)
- 22. The End