Title: Digital Signal Processing

Semester: First Semester M Tech (VLSI)

3-0-0,  3 Credits

Prerequisites:  Signals and Systems

Review of Signals and Systems basics, LTI systems, Convolution:

Continuous - Discrete time signals, Even-Odd signals, Periodic - Nonperiodic signals, Deterministic-Random signals, Energy-Power signals, (Continuous/Discrete) signals - unit step, unit impulse, sinusoidal and complex exponential signals. Operations on signals.

Representation, Linear-Nonlinear, Causal-Noncausal, Time invariant-Time variant, systems with memory, systems without memory; BIBO stability, Feedback system. LTI system – Response of LTI system, Convolution, Properties (Continuous/Discrete);

Fourier Representations (FS, FT, DTFS, DTFT, DFT) and Sampling:

Fourier series (FS) for periodic signals; Fourier transform (FT) - Properties of continuous time FT; Frequency response of continuous time LTI systems.

Discrete time Fourier series (DTFS) -Discrete Time Fourier transform (DTFT) - Properties of DTFT; Frequency response of discrete time LTI systems.

Sampling theorem, Reconstruction of signal, Aliasing, Sampling of discrete time signals;  Interrelationship amongst different representation and Transforms

Introduction to DFT: Discrete Fourier Transform and its relationship with DTFT.

Filtering, Filter Design, Adaptive filters:

Analog filter deisgn - Butterworth filter design (low pass)

IIR Filter Design: Impulse Invariant method, Bilinear Transformation, Butterworth filters

FIR: Filter Design, FIR using windowing

Realization structures: Direct from I, Direct form II

Introduction to adaptive filters (Wiener filters, Adaptive Wiener)

Text Books/References:

1. John G. Proakis and Dimitris K Manolakis, “Digital Signal Processing”, Prentice Hall, 4 edition, 2006.

2. Alan V. Oppenheim, Alan S. Willsky, S. Hamid Nawab, “Signals and Systems”, Prentice Hall India Private Limited, 1997.

3. Simon Haykin, Barry Van Veen, “Signals and Systems”, John Wiley and Sons, Wiley 2nd  Edition, 2005.