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.


56%: Lecture
44%: Practical (Laboratory)


20%: Coursework (Report)
80%: Examination (Unseen examination)

Contact hours and workload

This module is 150 hours of work. This breaks down into 36 hours of contact time and 114 hours of independent study.

This module is running in the academic year 2019/20. We also plan to offer it in future academic years. It may become unavailable due to staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of such changes to modules at the earliest opportunity.