Time domain analysis of discrete-time systems - Basic discrete time signals, operations and properties, mathematical view, Introduction to sampling, Nyquist theorem. Systems – properties, linear time invariant systems, impulse response, convolution, causality and stability. Difference equations. Transform domain analysis of discrete-time systems -Z Transform – definition and properties, ROC, transfer function, poles and zeroes, application to discrete systems. 

Representation of systems – signal flow graph, realization of z-domain transfer function. Frequency domain analysis of discrete-time systems -Fourier series and fourier transform. Relation between continuous and discrete time spectra, aliasing, reconstruction. DFS properties, Properties and applications of DTFT. Relationship between time, Z and frequency domains, Relation between frequency domain representation in continuous and discrete domain. Sampling in frequency domain, DFT, Properties of DFT. Linear convolution using DFT. FFT- DIT and DIF, Basics of Multirate signal processing Decimation and interpolation. Digital Filter Design- Characteristics of Digital Filters, Filter structures, FIR filter design – window method, frequency sampling method, Relation between S and Z domains, IIR filter design – Butterworth and Chebyshev