The interdisciplinary field of biomedical engineering requires its practitioners to master not only engineering skills, but also a diversity of material in the biological sciences. This text helps biomedical engineers strengthen their skills in the common network of applied mathematics that ties together these diverse disciplines. Based on the author's 30 years of experience in teaching as well as his personal research on neurosensory systems, Signals and Systems Analysis in Biomedical Engineering provides a ready source of information on those specialized mathematical techniques most useful in describing and analyzing biomedical signals, including ECG, EEG, blood pressure, biochemical spectrograms, and tomographic images.

Enriched with many examples that promote sound practical analysis, this book:

Presents the traditional systems mathematics used to characterize linear time-invariant (LTI) systems and, given inputs, find their outputs

Explains the relations between impulse response, real convolution, transfer functions and frequency response functions

Reviews specialized mathematical techniques used to characterize and model nonlinear systems

Introduces the basic mathematical tools used to describe noise and how it propagates through LTI and NLTI systems

Describes how signal-to-noise ratio can be improved by signal averaging and linear and nonlinear filtering

Contenuti:

INTRODUCTION TO BIOMEDICAL SIGNALS AND SYSTEMS
General Characteristics of Biomedical Signals
General Properties of Physiological Systems
Chapter Summary

REVIEW OF LINEAR SYSTEMS THEORY
Linearity; Causality, Stationarity
Analog Systems
Systems Described by Sets of ODEs
Linear System Characterization
Discrete Systems and Signals
Stability of Systems
Chapter Summary

THE LAPLACE TRANSFORM AND ITS APPLICATIONS
Introduction
Properties of the Laplace Transform
Some Examples of Finding Laplace Transforms
The Inverse Laplace Transform
Applications of the Laplace Transform
Chapter Summary

FOURIER SERIES ANALYSIS OF PERIODIC SIGNALS
Introduction
Properties of the Fourier Series
Fourier Series Examples
Chapter Summary

THE CONTINUOUS FOURIER TRANSFORM
Introduction
Properties of the CFT
Analog-to-Digital Conversion and the Sampling Theorem
The Analytical Signal and the Hilbert Transform
The Modulation Transfer Function in Imaging
Chapter Summary

THE DISCRETE FOURIER TRANSFORM
Introduction
The CFT, ICFT, DFT and IDFT
Data Window Functions
The FFT
Chapter Summary

INTRODUCTION TO TIME-FREQUENCY ANALYSIS OF BIOMEDICAL SIGNALS
Introduction
The Short-term Fourier Transform (STFT)
Gabor and Adaptive Gabor Transform
Wigner-Ville & Pseudo-Wigner Transforms
Cohen's General Class of JTF Distributions
Introduction to JTFA Using Wavelets
Applications of JTF Analysis to Physiological Signals
JTFA Software
Chapter Summary

INTRODUCTION TO THE ANALYSIS OF STATIONARY NOISE AND SIGNALS CONTAMINATED WITH NOISE
Introduction
Noise Descriptors and Noise in Systems
Calculation of Noise Descriptors with Finite Discrete Data
Signal Averaging and Filtering for Signal-to-Noise Ratio Improvement
Introduction to the Application of Statistics and Information Theory to Genomics
Chapter Summary

BASIC MATHEMATICAL TOOLS USED IN THE CHARACTERIZATION OF PHYSIOLOGICAL SYSTEMS
Introduction
Some General Properties of Physiological Systems
Some Properties of Nonlinear Systems
Physical Factors Determining the Dynamic Behavior of Physiological Systems
Means of Characterizing Physiological Systems
Chapter Summary

INTRODUCTION TO THE MATHEMATICS OF TOMOGRAPHIC IMAGING
Introduction
Algebraic Reconstruction
The Radon Transform
The Fourier Slice Theorem
The Filtered Back-Projection Algorithm (FBPA)
Chapter Summary

APPENDICES
Cramer's Rule
Signal Flow Graphs and Mason's Rule
Bode (Frequency Response) Plots
Computational Tools for Biomedical Signal Processing and Systems Analysis

BIBLIOGRAPHY AND REFERENCES
INDEX

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Signals and Systems Analysis in Biomedical Engineering

Northrop, Robert B.

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