Introduction to DSP; Basic discrete-time signals, operations, and properties, introduction to sampling, aliasing Discrete-time systems - properties, linear-time invariant systems, impulse response, convolution, correlation, causality and stability; Representation of LTI systems - difference equations, Z Transform: Definition and properties, ROC, inverse Z transform, transfer function, poles and zeros, relate system behaviour in time and frequency domains to pole-zero plot, Application of Z transforms to discrete-time systems, Representation of systems – signal flow graph, realisation of a Z-domain transfer function, Fourier series & Fourier transform, Discrete Fourier series (DFS), Properties of DFS, Relation between continuous and discrete time spectra, aliasing, reconstruction of continuous-time signal from samples, Discrete-time Fourier transform (DTFT), properties and applications of DTFT, Relationship between the three domains – h(n), H(z), H(), Sampling in frequency domain, Discrete Fourier Transform (DFT), DFT properties, linear convolution using DFT, Circular convolution, use of DFT in linear filtering, filtering of long data sequences, Efficient computation of DFT, Fast Fourier transform (FFT) algorithms – DIT, DIF, Characteristics of digital filters, Types, Filter Structures, design from pole-zero map, LPF, HPF and BPF, Digital resonators, Notch, and All-pass filters. FIR filter design: window method, frequency sampling method, optimal filter design, IIR filter design: H(s) H(z), Filter design using Butterworth, Chebyshev & Elliptic approximations, Direct design of IIR filters, Finite word length effects, Real-time implementation of SP algorithms - options, Application of DSP to Speech, Audio, Image, Video and Biomedical signal processing