Signals and systems
This is an undergraduate-level course taught at IIT-Kharagpur, providing 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 of the course contents (including lecture materials and problems) are borrowed from these textbooks.
Spring 2024
Grading: Quiz: 20%, mid-sem: 30%, final exam: 50%
The following is a rough outline of the contents that we will cover in this course. This course has no particular prerequisite, but a background in network analysis would help you grasp some of the concepts quickly.
Topics covered: Continuous-time (CT) and Discrete-time (DT) signals, operation on signals, sinusoid and exponential signals, periodicity, power and energy, unit impulse, step, and ramp signals, measure of signals, basic system properties: systems with and without memory, invertibility and inverse systems, causality, shift-invariance and linearity.
DT and CT linear shift-invariant (LSI) systems, representation of CT and DT signals in terms of impulse, impulse response of LSI systems and convolution integral, properties of LSI systems, causal LSI systems described by differential and difference equations and its block diagram and signal flow representations.
Response of LSI systems to complex exponentials, Fourier series representation of CT and DT periodic signals, convergence and properties of the Fourier series, Parseval's relation, induced gain of LSI systems, LSI systems with periodic inputs.
Representation of aperiodic signals: the CT and DT Fourier transform, its convergence and examples, properties of Fourier transform: convolution, multiplication and duality, a brief overview of Laplace transform.
Transfer function, concept of poles and zeros, causality and stability of LSI systems, block diagram representation of causal LSI systems with some examples of physical systems.
The z-transform, the region of convergence, properties of the z-transform, inverse z-transform, initial- and final-value theorems in the z-domain, transfer function in the z-domain, stability of LSI systems in the z-domain, block diagram representations of LSI systems in the z-domain.
Stochastic signals, stationarity, linear shift-invariant systems with stochastic input signals, power spectral density and the Wiener-Khinchin theorem, Nyquist sampling theorem for band-limited stochastic signals.
Problem Sets: