Digital Biosignal Processing

Module aims

In this module you will be introduced to the basic concepts and techniques for representing, transforming, and processing discrete-time signals. The module emphasises practical implementations of the theoretical concepts on biomedical applications. Specifically this module aims to provide you with:

An introduction to the fundamental principles for characterising discrete-time signals and systems

An understanding of methods for analysing and processing discrete-time signals

An opportunity to discuss and be exposed to relevant representative applications of biosignal processing

Learning outcomes

Upon successful completion of this module you will be able to:

1) Explain common concepts in biosignal processing including the sampling theorem, the effects of aliasing and the relations between the Fourier transform, the discrete-time Fourier transform, and the z-transform

2) Explain the relations between second order statistics and power spectral density (PSD) of discrete-time random signals

3) Describe the relations between sampling and periodicity in time and frequency domain

4) Employ the concept of a random signal to characterize experimental signals

5) Characterize linear time-invariant discrete-time systems with transfer functions

6) Apply basic design rules for FIR/IIR filters

7) Characterize a discrete-time random signal with second-order statistics and power spectral density

8) Critically apply appropriate methods to analyse experimental and discrete-time biomedical signals

Module syllabus

In this module you will cover the following topics: Sampling of continuous-time signals From continuous-time signals to discrete-time signals, Nyquist theorem; Discrete-time signals and systems Definition of discrete-time signals and systems, LTI discrete-time systems, convolution in discrete-time domain; Discrete-time Fourier transform and DFT Discrete-time Fourier transform and discrete Fourier transform, relations between continuous frequency and discrete frequency; Z-transform z-plane and relations between Fourier series, Fourier transform, Laplace transform, discrete-time Fourier transform, discrete Fourier transform (DFT), and z-transform; FIR/IIR filters Basic notions on FIR and IIR filter characterisation and design; Discrete-time random signals Introduction to random processes in the discrete-time domain and their characterisation with second-order statistics; Power spectral density (PSD) of discrete-time random signals Relation between auto-correlation function and PSD, spectrogram and correlogram; Estimation of PSD Estimates of PSD, bias and variance of estimate, Welch periodogram; Filtering discrete-time random signals PSD of random processes filtered by LTI systems.

Pre-requisites

Signals and Control Basics of complex numbers (canonical form; polar form; conjugation; modulus) Fourier transform of continuous time signals Laplace transform Convolution Probability density function of random variables, joint probability, expectation operator Matlab programming

Teaching methods

Lectures: 18 hours
Labs: 9 hours

Assessments

Examinations:

●  Written exam: Written exam -- Digital Biosignal Processing; 82% weighting

Rubrics: Parts 1 & 2, Part 1 is MCQ, Part 2 is 1 hour and 1 Q with subparts

Outline answers to past papers will be available

Courseworks:

●  Lab report: Lab exercises Report 1; 6% weighting; Processing of experimental biomedical signals using Matlab

●  Lab report: Lab exercises Report 2; 6% weighting; Processing of experimental biomedical signals using Matlab

●  Lab report: Lab exercises Report 3; 6% weighting; Processing of experimental biomedical signals using Matlab