This module provides practical coverage of the fundamentals of digital signal processing, with emphasis on the following key topics: the discrete Fourier transform, the z-transform and digital filter design.

TRANSFORMS: Review of the Fourier transform, its properties and the more general Laplace transform. Sampling and Railings leading to the z-transform for discrete signals. The DFT and its relationship to these transforms. SYSTEMS: Difference equations and the z-transform. Recursive and non-recursive systems and their z-plane descriptions. Examples: averaging filter, integrator, differentiator. Important properties; linear phase systems, all pass systems. SIGNAL WINDOWING: Choice of windows for reduced spectral leakage. The DFT as a signal analyser. Windowing in the DFT context. Padding with zeros to reduce picket-fence effect. NON-RECURSIVE FILTERS: Design by windowing methods. Sample design. RECURSIVE FILTERS: Design based on analogue prototypes. Bi-linear mapping approach and Impulse-invariant approach, their areas of suitability. Case studies. FILTER TRANSFORMATION: Transformations for BP and HP filters. Analogue and digital approaches. NOISE: Overview of noise issues and the correlation method. RATE CONVERSION: Introduction to up-sampling and down-sampling.SIGMA-DELTA methods in A/D and D/A conversion.

* Examine the various components of a typical DSP system and identify factors that influence their functionality, specifications and choice * Demonstrate how digital signal and data are represented in time and frequency domains, and deal with related qunatisation issues * Recognise, predict and quantify sources and levels of noise in DSP systems, and devise means to reduce noise effect * Apply the FFT and a choice of tapered windows to monitor and analyse signals correctly while minimising errors due to leakage and with due compensation for tapered window properties * Carry out various numerical computations related to implementation and analysis of key DSP operations, such as convolution and domain transformation * Recognise how key DSP algorithms are implemented for real-time applications and evaluate the effects of qunatisation and finite-word length

None

* Examine the behaviour of linear time-invariant systems as frequency selective-filters using convolution and FFT-based techniques * Design and model FIR and IIR digital filters to meet a given frequency response specification using the Window and Biline

The module is delivered via 2 lecture hours and 2 laboratory hours per week over 12 teaching weeks. Assessment is based 30% coursework and 70% final exam. Coursework comprises 3 lab-based assignments (20%) whereby students work in groups on a number of problems related to linear filtering of different types of signals, such as images and speech, and a mid-term test (10%). The main focus of the mid-tern test is on analysis and design problems and associated numerical computation. The lab assignments are designed to assess how the students select an approach, formulate an algorithm and implement it, using Matlab environment.