Digital Signal Processing

Overview

Signals and spectral representation, linear systems, Fourier and Laplace transform, convolution, impulse response, transfer function, sampled data, sampling theorem, design of analogue filters, infinite impulse response (IIR) filters, finite impulse response (FIR) filters, truncation and windowing. Decimation, interpolation, multi-rate processing. Discrete Fourier transform (DFT), fast Fourier transform (FFT), spectral analysis, FFT applications. Estimation theory, the Wiener filter, adaptive algorithms, recursive least squares, stochastic gradient algorithms.

Coursework:
1. Assignment 1: problem set (theory and practical Matlab elements)
2. Assignment 2: Digital filter design for noise removal from ECG signal (design in Matlab, submission via report)

Learning Objectives

• Application of elementary algebra, complex number theory, linear algebra, statistics, and calculus in the derivation and analysis of signal processing systems and algorithms.
• Digital IIR and FIR ideal filter design requires derivation (applying various maths techniques) of coefficients from given filter requirement data, considering application-related constraints on the global filter characteristics; the principles underlying the advantages and limitations of different approaches (e.g., Butterworth, Chebyshev, FIR linear-phase etc) need to be understood and applied. The derivation, choice (e.g., LMS vs RLS) and application of optimal and adaptive filtering techniques requires analysis and characterisation of the signal statistics as determined by the application scenario.
• Selecting appropriate techniques for calculation of convolution output; choice of appropriate window in DFT analysis; selection of filter type / mapping on the basis of given application criteria & requirements; selection of adaptive algorithm in adaptive filtering applications.
• CW2 involves communicating via a technical report the specific features, effectiveness, and limitations of the taken approach to address the ECG signal noise reduction problem.
• In most weeks, the tutorial questions require to addressing a problem both with theory and by validation in software.
• In CW2, the students study digital filter design independently, from a variety of sources and by a variety of techniques.
• Throughout the course, students design and write code for a wide range of signal processing algorithms
• CW1 and CW2 require students to manage their own learning and development including time management and organisational skills.

• In CW2, students need to articulate and effectively communicate the design and technological rationale for a chosen digital filter design in their technical reports.

Skills

• numeric
• problem solving
• design, implement and test digital filter designs in Matlab
• perform spectral analysis on signals

Assessment

None