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Preface | |
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About the Authors | |
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Introduction to Signal Processing | |
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Descriptions of Physical Data (Signals) | |
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Classification of Data | |
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Deterministic Signals | |
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Classification of Deterministic Data | |
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Periodic Signals | |
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Almost Periodic Signals | |
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Transient Signals | |
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Brief Summary and Concluding Remarks | |
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MATLAB Examples | |
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Fourier Series | |
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Periodic Signals and Fourier Series | |
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The Delta Function | |
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Fourier Series and the Delta Function | |
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The Complex Form of the Fourier Series | |
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Spectra | |
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Some Computational Considerations | |
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Brief Summary | |
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MATLAB Examples | |
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Fourier Integrals (Fourier Transform) and Continuous-Time Linear Systems | |
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The Fourier Integral | |
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Energy Spectra | |
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Some Examples of Fourier Transforms | |
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Properties of Fourier Transforms | |
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The Importance of Phase | |
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Echoes | |
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Continuous-Time Linear Time-Invariant Systems and Convolution | |
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Group Delay (Dispersion) | |
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Minimum and Non-Minimum Phase Systems | |
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The Hilbert Transform | |
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The Effect of Data Truncation (Windowing) | |
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Brief Summary | |
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MATLAB Examples | |
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Time Sampling and Aliasing | |
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The Fourier Transform of an Ideal Sampled Signal | |
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Aliasing and Anti-Aliasing Filters | |
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Analogue-to-Digital Conversion and Dynamic Range | |
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Some Other Considerations in Signal Acquisition | |
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Shannon's Sampling Theorem (Signal Reconstruction) | |
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Brief Summary | |
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MATLAB Examples | |
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The Discrete Fourier Transform | |
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Sequences and Linear Filters | |
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Frequency Domain Representation of Discrete Systems and Signals | |
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The Discrete Fourier Transform | |
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Properties of the DFT | |
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Convolution of Periodic Sequences | |
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The Fast Fourier Transform | |
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Brief Summary | |
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MATLAB Examples | |
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Introduction to Random Processes | |
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Random Processes | |
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Basic Probability Theory | |
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Random Variables and Probability Distributions | |
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Expectations of Functions of a Random Variable | |
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Brief Summary | |
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MATLAB Examples | |
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Stochastic Processes; Correlation Functions and Spectra | |
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Probability Distribution Associated with a Stochastic Process | |
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Moments of a Stochastic Process | |
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Stationarity | |
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The Second Moments of a Stochastic Process; Covariance (Correlation) Functions | |
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Ergodicity and Time Averages | |
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Examples | |
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Spectra | |
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Brief Summary | |
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MATLAB Examples | |
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Linear System Response to Random Inputs: System Identification | |
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Single-Input Single-Output Systems | |
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The Ordinary Coherence Function | |
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System Identification | |
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Brief Summary | |
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MATLAB Examples | |
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Estimation Methods and Statistical Considerations | |
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Estimator Errors and Accuracy | |
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Mean Value and Mean Square Value | |
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Correlation and Covariance Functions | |
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Power Spectral Density Function | |
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Cross-spectral Density Function | |
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Coherence Function | |
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Frequency Response Function | |
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Brief Summary | |
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MATLAB Examples | |
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Multiple-Input/Response Systems | |
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Description of Multiple-Input, Multiple-Output (MIMO) Systems | |
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Residual Random Variables, Partial and Multiple Coherence Functions | |
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Principal Component Analysis | |
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Proof of [characters not reproducible] | |
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Proof of [characters not reproducible] | |
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Wave Number Spectra and an Application | |
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Some Comments on the Ordinary Coherence Function [gamma superscript 2 subscript xy](f) | |
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Least Squares Optimization: Complex-Valued Problem | |
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Proof of H[subscript W](f) to H[subscript 1](f) as [kappa](f) to [infinity] | |
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Justification of the Joint Gaussianity of X(f) | |
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Some Comments on Digital Filtering | |
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References | |
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Index | |