EC21208 Signals and Systems

This undergraduate-level course taught at IIT Kharagpur provides a first exposure to signal processing through a principled study of signals and systems. The following are the two main textbooks followed in the course:

• Signals and Systems (2nd edition), A. V. Oppenheim, A. S. Willsky, and S. H. Nawab
• Principles of Signal Processing and Linear Systems (2nd edition), B. P. Lathi

Most course contents (including lecture materials and problems) are borrowed from these textbooks.

The following two resources are highly recommended if you are interested in a more mathematically principled treatment of Fourier analysis, which forms a significant part of the course:

• Fourier Analysis: An Introduction, Elias M. Stein and Rami Shakarchi
• The Fourier Transform and its Applications, Lecture notes by Brad Osgood, Stanford University (pdf)

Spring 2025-26

• Problem Set 1
• Problem Set 2
• Problem Set 3
• Problem Set 4
• Problem Set 5

Spring 2024-25

• Problem Set 1
• Problem Set 2
• Problem Set 3
• Problem Set 4
• Problem Set 5

Spring 2023-24

Grading: Quiz: 20%, mid-sem: 30%, final exam: 50%

The course has no particular prerequisite, though background in network analysis is helpful.

Topics covered:

• Continuous-time and discrete-time signals; signal operations; sinusoid and exponential signals; periodicity; power and energy; impulse, step, and ramp signals; signal measures; basic system properties
• Linear shift-invariant systems; impulse response and convolution; system descriptions via differential and difference equations
• Fourier series representation; convergence properties; Parseval's relation; LSI systems with periodic inputs
• Fourier transform (continuous and discrete time); convergence; properties including convolution, multiplication, and duality; Laplace transform overview
• Sampling of band-limited signals; Shannon-Nyquist sampling theorem; discrete-time processing of continuous-time signals
• Transfer functions; poles and zeros; causality and stability; block diagram representations
• Z-transform; region of convergence; properties; inverse z-transform; transfer functions in z-domain; stability analysis
• Stochastic signals; stationarity; power spectral density; Wiener-Khinchin theorem; sampling of stochastic signals

Problem sets:

• Problem Set 1
• Problem Set 2
• Problem Set 3
• Problem Set 4
• Problem Set 5
• Problem Set 6