This course aims to give a thorough grounding in the design of digital filters and in multirate signal processing techniques.

After attending this course, students will know how to specify, analyze and design digital filters for use in discrete time signal processing systems. They will know how to implement filters in hardware and software. They will also know how to analyze and design a signal processing system containing multiple sample rates and how to select the best sample rate to use in different parts of the system.

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.