# Biomedical Engineering (MEng)

## Digital Biosignal Processing

### Module aims

Digital Biosignal Processing begins with the introduction to the analysis of discrete-time deterministic signals and systems, including discrete-time convolution, the z-transform, the discrete-time Fourier transform, and digital filters. The course then introduces discrete-time stochastic processes, their characterization, and processing. The topics will be presented in relation to their biomedical applications, with examples from ECG, EMG, EEG, and other types of electrophysiological recordings. Each lecture will be followed by MATLAB exercises on real biomedical signals and problems

### Learning outcomes

Explain the sampling theorem and predict the effects of aliasing Describe the properties of linear time-invariant discrete-time systems Characterise linear time-invariant discrete-time systems with transfer functions Explain the relations between the Fourier transform, the discrete-time Fourier transform, and the z-transform Describe the structure of FIR and IIR filters Describe basic design rules for FIR/IIR filters Explain the concept of stochastic process and its use in characterising signals Characterise a discrete-time stochastic process with second-order statistics Explain the concept of power spectral density (PSD) of discrete-time stochastic processes Estimate PSD and filter biomedical signals Explain applications to biomedical signals Write simple MATLAB scripts for processing biomedical signals

### Module syllabus

Sampling of continuous-time signals Discrete-time signals and systems; Cyclic convolution Discrete time Fourier transform The z-transform; FIR/IIR filters Discrete-time stochastic processes; Characterisation by second-order statistics Power spectral density (PSD) of discrete-time stochastic processes Estimation of PSD by DFT and parametric methods Filtering discrete-time stochastic processes Non-stationary stochastic processes and short-time spectral estimation

### 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 (2hr): Short- and long-answer questions (10 questions in total) 82% weighting

Coursework:
●  Item 1:Lab report Title:Lab exercises Report 1 Description:Processing of experimental biomedical signals using Matlab Weighting: 6%
●  Item 2:Lab report Title:Lab exercises Report 2 Description:Processing of experimental biomedical signals using Matlab Weighting: 6%
●  Item 3:Lab report Title:Lab exercises Report 3 Description:Processing of experimental biomedical signals using Matlab Weighting: 6%

No type of previous exam answers or solutions will be available

Feedback : The reports on lab exercises will be evaluated and a feedback will be provided within two weeks from submission. The feedback will consist in specific comments to the reports, justifying the mark

### Supplementary

• #### Discrete-time signal processing

Oppenheim, Alan V.,

Third edition, Pearson new international edition., Pearson

• #### Discrete-time signal processing

Oppenheim, Alan V.,

Third edition, Pearson new international edition., Pearson

• #### Discrete-time signal processing / Alan V. Oppenheim, Ronald W. Schafer.

Oppenheim, Alan V.,

3rd ed., International ed., Pearson