To present the fundamental principles and applications of Digital Signal Processing

To enable students to gain an appreciation of sampling theory, z-transforms and system functions; to analyse and design digital filters using signal flow graphs, elementary FIR/IIR filter design techniques, windows and bilinear and band transformations; to gain an appreciation of discrete Fourier transforms; to perform and interpret correctly the results of simple and short-time spectral estimation; to see fast computation of the DFT as decimation -in-time; to gain an appreciation of linear, cyclic and sectioned convolution in the context of digitial filtering and to implement (fast) filtering algorithms; to develop basic multirate signal processing elements and identities and to see them applied in typical applications; to analyse and design sample rate changing systems; to gain an appreciation of maximally decimated filter banks, their limitations and the sources of errors therein.

Sampling theory, z-transforms, system functions. Digitial filter structures, signal flow graphs, elementary FIR/IIR filter design techniques, windows, bilinear and band transformations. Discrete Fourier transform, relationship between DFT and DTFT, simple and short-time spectral estimation, fast computation of DFT as decimation-in-time.
Linear convolution, cyclic convolution, sectioned convolution (overlap-add and overlap-save), application to fast filtering algorithms, windowing.
Basic multirate elements and identities, design of sample rate changing systems, polyphase representtion of filters, maximally decimated filter banks.