Practical Biomedical Signal Analysis Using MATLAB®

Katarzyna J. Blinowska, Jarosław Żygierewicz

• Publisher: CRC Press
• Year: 2021
• eBook ISBN: 9780429775727
• Edition: 2
• Topic: Medicine
• Subtopic: Physics
• Index: Physics

Covering the latest cutting-edge techniques in biomedical signal processing while presenting a coherent treatment of various signal processing methods and applications, this second edition of Practical Biomedical Signal Analysis Using MATLAB ® also offers practical guidance on which procedures are appropriate for a given task and different types of data.

It begins by describing signal analysis techniques—including the newest and most advanced methods in the field—in an easy and accessible way, illustrating them with Live Script demos. MATLAB® routines are listed when available, and freely available software is discussed where appropriate. The book concludes by exploring the applications of the methods to a broad range of biomedical signals while highlighting common problems encountered in practice.

These chapters have been updated throughout and include new sections on multiple channel analysis and connectivity measures, phase-amplitude analysis, functional near-infrared spectroscopy, fMRI (BOLD) signals, wearable devices, multimodal signal analysis, and brain-computer interfaces.

By providing a unified overview of the field, this book explains how to integrate signal processing techniques in biomedical applications properly and explores how to avoid misinterpretations and pitfalls. It helps readers to choose the appropriate method as well as design their own methods. It will be an excellent guide for graduate students studying biomedical engineering and practicing researchers in the field of biomedical signal analysis.

Features:

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• Fully updated throughout with new achievements, technologies, and methods and is supported with over 40 original MATLAB Live Scripts illustrating the discussed techniques, suitable for self-learning or as a supplement to college courses

• 
  
  

• Provides a practical comparison of the advantages and disadvantages of different approaches in the context of various applications

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• Applies the methods to a variety of signals, including electric, magnetic, acoustic, and optical

Katarzyna J. Blinowska is a Professor emeritus at the University of Warsaw, Poland, where she was director of Graduate Studies in Biomedical Physics and head of the Department of Biomedical Physics. Currently, she is employed at the Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. She has been at the forefront in developing new advanced time-series methods for research and clinical applications.

Jaros?aw ?ygierewicz is a Professor at the University of Warsaw, Poland. His research focuses on developing methods for analyzing EEG and MEG signals, brain-computer interfaces, and applications of machine learning in signal processing and classification.

1A Short Introduction to MATLAB®

DOI: 10.1201/9780429431357-1

1.1 Introduction

MATLAB® is a commercial platform offered by The MathWorks, Inc., the USA which delivers a high-level, matrix-based language and an integrated development environment. Together with specialized libraries, so-called toolboxes, it is a very efficient system for fast prototyping, and complex scientific and engineering computations. What is also very important many algorithms used in biomedical signal processing were implemented and published as MATLAB functions or toolboxes. In the following sections, we shortly present basic syntax and concepts, needed for the understanding of the examples given in the book and in accompanying Live Script demos. This may be helpful for a novice MATLAB user. A deeper knowledge of MATLAB can be obtained from many MATLAB books and the very useful build-in documentation system of MATLAB.

1.2 Where Is Help?

The documentation can be accessed by the GUI, or from the command prompt. In the latter case just type doc (this opens the graphical documentation window) or help (if you prefer a more compact textual help). The general set of commands can be displayed by issuing doc matlab/general.

1.3 Vectors and Matrixes

In signal processing, it is very convenient to implement the signals as vectors or matrixes. The most basic type of variable in MATLAB is a matrix. In fact, a scalar value is represented as $1\times 1$ matrix. So vectors are $N\times 1$ (a column vector) or $1\times N$ (a row vector).

The matrixes can be entered either from command line/editor (type and execute the examples in the command line, and look into the workspace window):

A=[1 2 3 4; 5 6 7 8; 8 9 1 2];

disp(A)

or produced by a function:

B=rand(3,3);

disp(B)

or, in practical cases most often, loaded from a file (this we will show later in Sect. 1.8).

Note the semicolon at the end of each line—it prevents MATLAB from displaying its result in the command window. A semicolon inside the matrix forming command finishes a given row and starts another one.

1.4 Matrix Operations

1.4.1 Algebraic Operations

In an intuitive way we can do the matrix algebraic operations:

B = [1 2;3 4];

disp(B)

C = B + B;

disp(C)

D = C - 2* B;

disp(D)

M = B/B;

disp(M)

An operator preceded by a dot evaluates the operation element-wise. Please, compare results of:

G = B*B;

disp(G)

H = B.*B;

disp(H)

There is a set of matrix operators. The basic ones are:

• transpose: B_tr = B';
• determinant: d = det(B);
• trace: d = trace(B);
• diagonal: di = diag(B);
• inverse: B_inv = B(̂-1);
• sum: s = sum(B); this sums by default along the first dimension, other direction can be indicated in the function call e.g., s = sum(B,2);

1.4.2 Matrix Indexing

Matrix addressing starts from 1. We get an element of a matrix like this:

B = [1 2;3 4];

disp(B)

1 2

3 4

>> B(1,2)

ans =

2

We assign its value in this way:

>> B(1,2) = 4;

>> B

B =

1 4

3 4

Note, that when you modify matrix elements, the matrix size adjusts automatically and it can create elements that were not directly assigned, setting them to 0. Note the element B(2,3) in the example below:

>> B(1,3) = 4;

>> B

B =

1 4 4

3 4 0

Range control is done only when retrieving matrix element...

Table of contents

• Cover Page
• Half-Title Page
• Series Page
• Title Page
• Copyright Page
• Contents
• About the Series
• Preface
• List of Abbreviations
• 1 A Short Introduction to MATLAB®
• 2 Introductory Concepts
• 3 Single Channel (Univariate) Signal
• 4 Multiple Channels (Multivariate) Signals
• 5 Application to Biomedical Signals
• Bibliography
• Index