# Advanced Digital Signal Processing (102H6)

15 credits, Level 7 (Masters)

Autumn teaching

This module will provide an overview of the applications of digital signal processing techniques.
It will include revision of:

• Fourier series, complex notation, linear systems theory, discretisation, transform techniques, Fourier series to Fourier integral, Fourier transform properties
• Complex frequency, Laplace transform, the Dirac delta functional, sampled data systems, z-transform, the inverse z-transform, the relationship between z and s planes, stability, poles and zero locations; Nyquist sampling theorem, aliasing, signal reconstruction from sampled data.

Detailed discussion of:

• system response and convolution
• correlation and convolution theorems, the matched filter
• digital filtering, system discrete transfer function, filter types, IIR and FIR, impulse response, methods of digital filter realisation
• IIR digital filter design, impulse invariant and bilinear transformation methods, designed from prototype normalised Butterworth and Chebychev analogue prototype filters
• FIR filters, the discrete Fourier transform and its properties
• FIR filter design, spectral leakage, window functions, sources of error in digital filter implementations, filter stability
• the fast Fourier transform
• extension of discrete Fourier transform and convolution theorem to two dimensions
• numerical computation of two dimensional frequency spectrum as a sequence of one dimensional discrete Fourier transforms.
• two dimensional filtering and impulse response, two dimensional convolution and correlation in the space and the frequency domains, applications to image and video processing
• discrete cosine transform in two dimensions, applications to image compression
• overview of the architecture of modern DSP hardware.

Matlab DSP Laboratory, overview of Matlab modelling:

1) Generation of a complex exponential sequence
2) Use of a moving average filter to smooth signal corrupted by noise
3) Convolution and correlation of two sequences
4) Computation of 1-D DFT
5) Computation of DFT using decimation in time FFT
6) IIR filter design using Matlab DSP filter design toolbox
7) FIR filter design using Matlab DSP filter design toolbox

Problem Section:

• Four problems of increasing difficulty (up-dated each year) solved by documented Matlab code for final report.

### Teaching and assessment

We’re currently reviewing teaching and assessment of our modules in light of the COVID-19 situation. We’ll publish the latest information as soon as possible.