Engineering and design
Advanced Digital Signal Processing
Module code: 102H6
Level 7 (Masters)
15 credits in autumn teaching
Teaching method: Lecture, Laboratory
Assessment modes: Coursework, Unseen examination
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
- Four problems of increasing difficulty (up-dated each year) solved by documented Matlab code for final report.
Module learning outcomes
- Understand the mathematics and concepts used in linear systems theory
- Understand the mathematics and concepts used in discretely sampled data systems
- Design from a given specification an IIR filter
- Design from a given specification an FIR filter