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Module details for 2022/23.

15 credits

FHEQ Level 7 (Masters)

Module Outline

Overview of the applications of digital signal processing techniques
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 commands.
8 Matlab m-files given illustrating Matlab coding of important signal processing operations:
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.

AHEP4 Learning Outcomes
M1, M2, M3, M4, M12

Library

P. Lynn, W. Fuerst, "Introductory Digital Signal Processing", Wiley, 1994.
E. Ifeachor, B. Jervis, "Digital Signal Processing, A Practical Approach", Addison Wesley, 1996.
J. Proakis, D. Manolakis, "Digital Signal processing", Prentics Hall, 1996
S. Mitra, "Digital Signal Processing ", McGraw-Hill, 2006
E. Brigham, "The Fast Fourier Transform and its Applications", Prentice-Hall, 1988

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

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Timing

Submission deadlines may vary for different types of assignment/groups of students.

Weighting

Coursework components (if listed) total 100% of the overall coursework weighting value.

How to read the week pattern

The numbers indicate the weeks of the term and how many events take place each week.

Dr William Wang

Assess convenor
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