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Course Co-ordinated by IIT Madras
Prof. V.G.K. Murti
IIT Madras


C. S. Ramalingam
IIT Madras


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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



Signals, Systems, Networks

  1. Introduction to Systems, Signals, Networks
  2. Representation and classification of systems
  3. Linear systems, time-invariance and causality
  4. Elementary signals: DC, sinusoidal, exponential, unit step, unit ramp, unit impulse or delta function
  5. Complex frequencies of signals
  6. Basic discrete-time signals
  7. Characterization of a linear system
  8. Impulse response
  9. Convolution, Evaluation of convolution



Fourier series

  1. Evaluating Fourier series coefficients
  2. Symmetry conditions
  3. Application to network analysis
  4. Exponential Fourier series
  5. Frequency spectrum
  6. Use of impulses in evaluating Fourier series coefficients
  7. Power and related ideas
  8. Convergence of Fourier series
  9. Properties of Fourier series



Continuous-time Fourier transform

  1. From Fourier series to Fourier transform
  2. Fourier transform: definition and examples
  3. Properties of Fourier transform
  4. Energy considerations
  5. Continuous-time Fourier transform of signals that are not absolutely integrable
  6. Continuous-time Fourier trasnform of periodic signals
  7. Continuous-time Fourier transform of unit step function and signum function
  8. Continuous-time Fourier transform of truncated sinusoid
  9. Convolution property of Fourier transform
  10. Application of continuous-time Fourier transform to system analysis



Laplace transforms

  1. Introduction and definition
  2. Laplace transforms of important functions: unit impulse, unit step, poles/zeros, notation
  3. Properties: Linearity, differentiation in the time domain
  4. Application of Laplace transform methods to circuit elements
  5. 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
  6. Laplace transform of periodic functions
  7. Inverse Laplace transformation
  8. Partial fraction expansion: simple poles, multiple poles
  9. Inverse Laplace transform by contour integration
  10. Relationship between Laplace and Fourier transforms


Applications of Laplace transform

  1. Applications of Laplace transform to network transients
  2. Circuit analysis: Resistor, Mutual inductance
  3. Example of Laplace transform method: Circuit with sinusoidal input, discontinuous current, discontinuous source
  4. Advantages of Laplace transform approach
  5. Application of Laplace transform method to a general LTI system
  6. The many facets of the system function H(s)
  7. Frequency response and stability
  8. System analysis example: find impulse response, system function, response to exponential input, steady-state response to a sinusoid

  1. Basic electrical circuits
  2. Calculus

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