To introduce the theory of digital signal processing, including the following very important topics: the discrete Fourier Transform, the Z-transform and digital ?lter design.

Discrete signals and systems. The DFT, its properties and applications; relationship to other transforms; Fourier, Laplace, Z-transform etc. Railings as theoretical samplers. Spectral descriptions of sequences. Analogue and digital convolution, the z-transform in the design of FIR digital ?lters. Linear-phase, all-pass ?lters, minimum-phase ?lters. Differentiators and Integrators. Windowing techniques in ?lter design. Filter design and fast convolution by FFT. Frequency-sampling ?lters. IIR ?lters: mapping from analogue ?lters, bi-linear mapping, review of other mappings, their application in digital and sampled-data (e.g. switched-capacitor) ?lters. Up-sampling and down-sampling. Band-pass signals and modulation. Finite word-length effects; impact on architectures. Noise topics. Sigma-delta noise shaping, applications in A/D and D/A conversion. Correlation principles. Fast correlation by DFT. Introduction to adaptive ?ltering. Wiener ?lter. LMS algorithm. Selected applications. Power spectra and spectral estimation.

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 Make use of the FFT to achieve large speed improvements in the correlation and ?ltering of data sets. Make use of the FFT and a choice of tapered windows to monitor signals correctly while minimizing errors due to leakage and with due compensation for tapered window properties. Model ?lters in the frequency domain, using the Z-transform, for both FIR and IIR ?lter types. Derive digital ?lters from analogue prototypes using common methods such as the Bilinear trasformation. Recognise, predict and quantify sources and levels of noise in DSP systems, and devise means to reduce noise effect.

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The module is based on 12 teaching weeks and delivered via a set of lectures, labs and seminars. Assessment is based on 80% final exam and 20% coursework which involves 3 assignments.