Basic elements of digital signal processing, comparison of analog and digital signal processing, multi-channel and multi-dimensional signals, random and deterministic signals, FIR and IIR systems, recursive and non-recursive systems, correlation of discrete time signals.

Frequency domain sampling and reconstruction of discrete time signals, DFT, DFT as linear transformation, frequency analysis of signals using DFT, properties of DFT, circular convolution, linear filtering methods based on DFT, overlap save and overlap add method, FFT algorithms, decimation in time and decimation in frequency algorithms, applications of FFT algorithms, linear filtering approach to computation of the DFT, Goertzel algorithm.

Structures for the realization of LTI systems, recursive and non-recursive realization of FIR systems, structures for FIR systems, direct form, cascade form, frequency sampling and lattice structures, structures for IIR systems, direct form, signal flow graphs and transposed structure, cascade, parallel form and lattice structures.

Introduction, LTI systems as frequency selective filters, Paley-Wiener theorem, characteristics of frequency selective filters, design of linear phase FIR filters, design of digital filters by placement of poles and zeros in z-plane, digital resonators, Notch filters, Comb filters and all pass filters, design of linear phase FIR filters using windows and by frequency sampling method.

Introduction, design of IIR filters from their analog counterparts, design using approximation of derivatives, impulse invariance, bilinear transformation and matched z-transformation, frequency transformations in analog and digital domains, design of digital filters based on least squares method, design of IIR filters in frequency domain.