# Biomedical Engineering (MEng)

## Digital Biosignal Processing

### Module aims

This course will introduce the basic concepts and techniques for representing, transforming, and processing discrete-time signals. The course emphasizes practical implementations of the theoretical concepts on biomedical applications.

The course specifically aims at:

·         Introducing the fundamental principles for characterizing discrete-time signals and systems

·         Presenting methods for analysing and processing discrete-time signals

·         Discussing and demonstrating relevant representative applications of biosignal processing

### Learning outcomes

Knowledge and Understanding

•               Explain the sampling theorem and predict the effects of aliasing

•               Explain the relations between the Fourier transform, the discrete-time Fourier transform, and the z-transform

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

Intellectual Skills

•               Understand the relations between sampling and periodicity in time and frequency domain

•               Understand the concept of random signal and its use in characterizing experimental signals

Practical Skills
• Characterize linear time-invariant discrete-time systems with transfer functions
• Apply basic design rules for FIR/IIR filters
• Characterize a discrete-time random signal with second-order statistics and power spectral density
• Analyse and process discrete-time biomedical signals

Transferable Skills

•               Represent and analyse experimental biomedical signals; identify appropriate analysis methods

### Module syllabus

• 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 characterization and design;
• Discrete-time random signals - Introduction to random processes in the discrete-time domain and their characterization 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 (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