Introduction to Applied Statistical Signal Analysis Guide to Biomedical and Electrical Engineering Applications 3rd Edition by Richard Shiavi 0120885816 9780120885817

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ISBN 10: 0120885816

ISBN 13: 9780120885817

Author: Richard Shiavi

Introduction to Applied Statistical Signal Analysis is designed for the experienced individual with a basic background in mathematics, science, and computer. With this predisposed knowledge, the reader will coast through the practical introduction and move on to signal analysis techniques, commonly used in a broad range of engineering areas such as biomedical engineering, communications, geophysics, and speech.

Introduction to Applied Statistical Signal Analysis intertwines theory and implementation with practical examples and exercises. Topics presented in detail include: mathematical bases, requirements for estimation and detailed quantitative examples for implementing techniques for classical signal analysis. This book will help readers understand real-world applications of signal analysis as they relate to biomedical engineering.

The presentation style is designed for the upper level undergraduate or graduate student who needs a theoretical introduction to the basic principles of statistical modeling and the knowledge to implement them practically.

· Accompanied by MATLAB notebooks that provide an interactive mode of learning which can be utilized by professors or independent learners, available from the Companion website.
· Includes over one hundred worked problems and real world applications. Many of the examples and exercises in the book use measured signals, many from the biomedical domain. Copies of these are available for download from the Companion website.

Introduction to Applied Statistical Signal Analysis Guide to Biomedical and Electrical Engineering Applications 3rd Table of contents:

Chapter 1 Introduction and terminology

1.1 Introduction

1.2 Signal terminology

1.2.1 Domain Types

1.2.2 Amplitude Types

1.2.3 Basic Signal Forms

1.2.4 The Transformed Domain—The Frequency Domain

1.2.5 General Amplitude Properties

1.3 Analog to digital conversion

1.4 Measures of signal properties

1.4.1 Time Domain

1.4.2 Frequency Domain

References

Chapter 2 Empirical modeling and approximation

2.1 Introduction

2.2 Model development

2.3 Generalized least squares

2.4 Generalities

2.5 Models from linearization

2.6 Orthogonal polynomials

2.7 Interpolation and extrapolation

2.7.1 Lagrange Polynomials

2.7.2 Spline Interpolation

2.8 Overview

References

Exercises

Chapter 3 Fourier analysis

3.1 Introduction

3.2 Review of fourier series

3.2.1 Definition

3.2.2 Convergence

3.3 Overview of fourier transform relationships

3.3.1 Continuous versus Discrete Time

3.3.2 Discrete Time and Frequency

3.4 Discrete fourier transform

3.4.1 Definition Continued

3.4.2 Partial Summary of DFT Properties and Theorems

3.5 Fourier analysis

3.5.1 Frequency Range and Scaling

3.5.2 The Effect of Discretizing Frequency

3.5.3 The Effect of Truncation

3.5.4 Windowing

3.5.5 Resolution

3.5.6 Detrending

3.6 Procedural summary

3.7 Selected applications

References

Exercises

Appendices

Appendix 3.1 DFT of ionosphere data

Appendix 3.2 Review of properties of orthogonal functions

Appendix 3.3 The fourier transform

Appendix 3.4 Data and spectral windows

Chapter 4 Probability concepts and signal characteristics

4.1 Introduction

4.2 Introduction to random variables

4.2.1 Probability Descriptors

4.2.2 Moments of Random Variables

4.2.3 Gaussian Random Variable

4.3 Joint probability

4.3.1 Bivariate Distributions

4.3.2 Moments of Bivariate Distributions

4.4 Concept of sampling and estimation

4.4.1 Sample Moments

4.4.2 Significance of the Estimate

4.5 Density function estimation

4.5.1 General Principle for χ2 Approach

4.5.2 Detailed Procedure for χ2 Approach

4.5.3 Quantile-Quantile Approach

4.6 Correlation and regression

4.6.1 Estimate of Correlation

4.6.2 Simple Regression Model

4.7 General properties of estimators

4.7.1 Convergence

4.7.2 Recursion

4.7.3 Maximum Likelihood Estimation

4.8 Random numbers and signal characteristics

4.8.1 Random Number Generation

4.8.2 Change of Mean and Variance

4.8.3 Density Shaping

References

Exercises

Appendices

Appendix 4.1 Plots and formulas for five probability density functions

Chapter 5 Introduction to random processes and signal properties

5.1 Introduction

5.2 Definition of stationarity

5.3 Definition of moment functions

5.3.1 General Definitions

5.3.2 Moments of Stationary Processes

5.4 Time averages and ergodicity

5.5 Estimating correlation functions

5.5.1 Estimator Definition

5.5.2 Estimator Bias

5.5.3 Consistency and Ergodicity

5.5.4 Sampling Properties

5.5.5 Asymptotic Distributions

5.6 Correlation and signal structure

5.6.1 General Moving Average

5.6.2 First-Order MA

5.6.3 Second-Order MA

5.6.4 Overview

5.7 Assessing stationarity of signals

5.7.1 Multiple Segments—Parametric

5.7.2 Multiple Segments—Nonparametric

References

Exercises

Appendices

Appendix 5.1 Variance of autocovariance estimate

Appendix 5.2 Stationarity tests

Chapter 6 Random signals, linear systems, and power spectra

6.1 Introduction

6.2 Power spectra

6.2.1 Empirical Approach

6.2.2 Theoretical Approach

6.3 System definition review

6.3.1 Basic Definitions

6.3.2 Relationships between Input and Output

6.4 Systems and signal structure

6.4.1 Moving Average Process

6.4.2 Structure with Autoregressive Systems

6.4.3 Higher-Order AR Systems

6.5 Time series models for spectral density

References

Exercises

Chapter 7 Spectral analysis for random signals: Nonparametric methods

7.1 Spectral estimation concepts

7.1.1 Developing Procedures

7.1.2 Sampling Moments of Estimators

7.2 Sampling distribution for spectral estimators

7.2.1 Spectral Estimate for White Noise

7.2.2 Sampling Properties for General Random Processes

7.3 Consistent estimators—Direct methods

7.3.1 Periodogram Averaging

7.3.2 Confidence Limits

7.3.3 Summary of Procedure for Spectral Averaging

7.3.4 Welch Method

7.3.5 Spectral Smoothing

7.3.6 Additional Applications

7.4 Consistent estimators—Indirect methods

7.4.1 Spectral and Lag Windows

7.4.2 Important Details for Using FFT Algorithms

7.4.3 Statistical Characteristics of BT Approach

7.5 Autocorrelation estimation

References

Exercises

Appendices

Appendix 7.1 Variance of periodogram

Appendix 7.2 Proof of variance of BT spectral smoothing

Appendix 7.3 Window characteristics

Appendix 7.4 Lag window functions

Appendix 7.5 Spectral estimates from smoothing

Chapter 8 Random signal modeling and parametric spectral estimation

8.1 Introduction

8.2 Model development

8.3 Random data modeling approach

8.3.1 Basic Concepts

8.3.2 Solution of General Model

8.3.3 Model Order

8.3.4 Levinson-Durbin Algorithm

8.3.5 Burg Method

8.3.6 Summary of Signal Modeling

8.4 Power spectral density estimation

8.4.1 Definition and Properties

8.4.2 Statistical Properties

8.4.3 Other Spectral Estimation Methods

8.4.4 Comparison of Nonparametric and Parametric Methods

References

Exercises

Appendices

Appendix 8.1 Matrix form of Levinson-Durbin recursion

Chapter 9 Theory and application of cross correlation and coherence

9.1 Introduction

9.2 Properties of cross correlation functions

9.2.1 Theoretical Function

9.2.2 Estimators

9.3 Detection of time-limited signals

9.3.1 Basic Concepts

9.3.2 Application of Pulse Detection

9.3.3 Random Signals

9.3.4 Time Difference of Arrival

9.3.5 Marine Seismic Signal Analysis

9.3.6 Procedure for Estimation

9.4 Cross spectral density functions

9.4.1 Definition and Properties

9.4.2 Properties of Cross Spectral Estimators

9.5 Applications

9.6 Tests for correlation between time series

9.6.1 Coherence Estimators

9.6.2 Statistical Properties of Estimators

9.6.3 Confidence Limits

9.6.4 Procedure for Estimation

9.6.5 Application

References

Exercises

Chapter 10 Envelopes and kernel functions

10.1 The Hilbert transform and analytic functions

10.1.1 Introduction

10.1.2 Hilbert Transform

10.1.3 Analytic Signal

10.1.4 Discrete Hilbert Transform

10.2 Point processes and continuous signals via kernel functions

10.2.1 Concept

10.2.2 Nerve Activity and the Spike Density Function

References

Exercises

Appendices

Table A Values of the Standardized Normal cdf Φ(z)

Table B Student’s t Distribution

Table C Chi-Square Distribution

Table D Critical Points for the Q-Q Plot Correlation Coefficient Test for Normality

Table E F Distribution Significance Limit for 97.5th Percentile

Table F Percentage Points of Run Distribution

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