Signals and Systems Analysis In Biomedical Engineering

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

Table of Contents:
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