Networks, signals and systems form the basic foundations of electrical engineering. Any electrical engineering product handles signals using electrical networks and circuits, which are called systems. Having a good understanding of signals and their time/frequency domain characterization is an absolute must for any electrical engineer. This course is a basic introduction to discrete and continuous-time signals, Fourier series, Fourier transforms and Laplace transforms.

Week. No

Topics

1.

Signals, Systems, Networks

Introduction to Systems, Signals, Networks

Representation and classification of systems

Linear systems, time-invariance and causality

Elementary signals: DC, sinusoidal, exponential, unit step, unit ramp, unit impulse or delta function

Complex frequencies of signals

Basic discrete-time signals

Characterization of a linear system

Impulse response

Convolution, Evaluation of convolution

2.

Fourier series

Evaluating Fourier series coefficients

Symmetry conditions

Application to network analysis

Exponential Fourier series

Frequency spectrum

Use of impulses in evaluating Fourier series coefficients

Power and related ideas

Convergence of Fourier series

Properties of Fourier series

3.

Continuous-time Fourier transform

From Fourier series to Fourier transform

Fourier transform: definition and examples

Properties of Fourier transform

Energy considerations

Continuous-time Fourier transform of signals that are not absolutely integrable

Continuous-time Fourier trasnform of periodic signals

Continuous-time Fourier transform of unit step function and signum function

Continuous-time Fourier transform of truncated sinusoid

Convolution property of Fourier transform

Application of continuous-time Fourier transform to system analysis

4.

Laplace transforms

Introduction and definition

Laplace transforms of important functions: unit impulse, unit step, poles/zeros, notation

Properties: Linearity, differentiation in the time domain

Application of Laplace transform methods to circuit elements

Properties of Laplace transforms: Multiplication by `t', integration, application to circuit elements, shift in `s' domain, shift in time domain, scaling, division by `t', initial value theorem, final value theorem, convolution in time domain

Laplace transform of periodic functions

Inverse Laplace transformation

Partial fraction expansion: simple poles, multiple poles

Inverse Laplace transform by contour integration

Relationship between Laplace and Fourier transforms

5.

Applications of Laplace transform

Applications of Laplace transform to network transients

Circuit analysis: Resistor, Mutual inductance

Example of Laplace transform method: Circuit with sinusoidal input, discontinuous current, discontinuous source

Advantages of Laplace transform approach

Application of Laplace transform method to a general LTI system

The many facets of the system function H(s)

Frequency response and stability

System analysis example: find impulse response, system function, response to exponential input, steady-state response to a sinusoid

Basic electrical circuits

Calculus

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