Filtering is an essential operation for manipulating signals of any kind. Filtering operations are used to extract essential information from real-life signals for analysis. This module will give you a thorough grounding in the design of digital filters and in multirate signal processing techniques. You will learn how to design filters by operating in either the time-domain or the frequency domain. You will learn about decomposing signals using filter-banks.

On successfully completing this module you should be able to, 1) apply various signal processing operations to discrete-time signals using a principled approach. 2) analyze digital signals in time domain and related transform domains, e.g. Fourier, Z-transform, and discrete cosine transform. 3) specify, analyze and design digital filters for use in discrete time signal processing systems; this includes both finite and infinite impulse response filters. 4) implement filters in hardware and software; 5) design multi-rate systems based on filter-bank operations.

Transforms: Discrete-time Fourier Transform (DTFT), Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT), Modified DCT (MDCT); Discrete Time systems: linear and circular convolution, overlap add, overlap save, stability triangle, allpass filters, group delay, minimum phase systems; FIR filter design: windowing, remez exchange algorithm for optimal design; IIR filter design: bilinear transformation, spectral transformations, optimal filter design; Filter implementation: coefficient quantisation, lattice filters; Multirate signal processing: sample rate conversion, polyphase filters, Farrow filters, subband processing.