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# Signals and Systems

### Overview

Instructor: Prof. K.S. Venkatesh, Department of Electrical Engineering, IIT Kanpur.

This course is a study of signals and systems, covering topics: formal definition of 'signal' and 'system', continuous and discrete signals, continuous and discrete-time systems, Linear Time-Invariant (LTI) systems, representation of continuous and discrete-time convolution, differential equations, difference equations, filters, periodic signals, Fourier series, Fourier transform and its properties, discrete-time Fourier transform, frequency response of continuous and discrete LTI systems, sampling, Laplace transform and its properties, inverse Laplace transform, z-transform and its properties, inverse z-transform.

### Syllabus

Lecture-01 Signals.
Lecture-02 Domain & Range of signal.
Lecture-03 System Introduction.
Lecture-04 Signal Properties.
Lecture-05 Frequently used continuous signals.
Lecture-06 Frequently used discrete time signals.
Lecture-07 Transformations on time & Range.
Lecture-08 System Properties.
Lecture-09 System Properties.
Lecture-10 Communiction Diagram As a Test For Linearity & Time Invariance.
Lecture-11 LTI system.
Lecture-12 Representation of Discrete Time Convolution.
Lecture-13 Representation Of Continuous Time Convolution.
Lecture-14 Properties of Convolution.
Lecture-15 Differential Equations.
Lecture-16 Solving Differential Equation.
Lecture-17 Physical System Relation With Differential Equation.
Lecture-18 System Described by Differential Equation.
Lecture-19 System Described by Differential Equation.
Lecture-20 Difference Equation Intro.
Lecture-21 LTI Systems Described By Difference Equation.
Lecture-22 Filters.
Lecture-23 Implementation with Integrators.
Lecture-24 Theory of Signal Representation.
Lecture-25 Representation of Periodic Signal.
Lecture-26 Fourier Series.
Lecture-27 Fourier Spectrum.
Lecture-28 Fourier Transform.
Lecture-29 Properties of CTFT.
Lecture-30 Properties of CTFT.
Lecture-31 Frequency Response of Continuous System.
Lecture-32 Discrete Signals & System Representation.
Lecture-33 Discrete Time Fourier Transform.
Lecture-34 Properties of Discrete Time Fourier Transform.
Lecture-35 Frequency Response of Discrete LTI System.
Lecture-36 Ideal Sampling.
Lecture-37 Flat Top Sampling.
Lecture-38 Faithful Sampling.
Lecture-39 Interpolation.
Lecture-40 Laplace Transform.
Lecture-41 Inverse Laplace Transform.
Lecture-42 Properties of Laplace Transform.
Lecture-43 Z-Transform.
Lecture-44 Inverse Z Transform.
Lecture-45 Properties of Z Transform.

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