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cohen l time frequency analysis theory applications 1995

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Textbook in PDF format Featuring traditional coverage as well as new research results that, until now, have been scattered throughout the professional literature, this book brings together—in simple language—the basic ideas and methods that have been developed to study natural and man-made signals whose frequency content changes with time—e.g., speech, sonar and radar, optical images, mechanical vibrations, acoustic signals, biological/biomedical and geophysical signals. Covers time analysis, frequency analysis, and scale analysis; time-bandwidth relations; instantaneous frequency; densities and local quantities; the short time Fourier Transform; time-frequency analysis; the Wigner representation; time-frequency representations; computation methods; the synthesis problem; spatial-spatial/frequency representations; time-scale representations; operators; general joint representations; stochastic signals; and higher order time-frequency distributions. Illustrates each concept with examples and shows how the methods have been extended to other variables, such as scale. For engineers, acoustic scientists, medical scientists and developers, mathematicians, physicists, and mangers working in the fields of acoustics, sonar, radar, image processing, biomedical devices, communication. Preface Notation in Brief The Time and Frequency Description of Signals Time Description of Signals. Frequency Description of Signals. Simple Calculation Tricks. Bandwidth Equation. AM and FM Contributions to the Bandwidth. Duration and Mean Tune in Terms of the Spectrum. The Covariance of a Signal. The Fourier Transform of the Time and Frequency Densities. Nonadditivity of Spectral Properties. Classification of Signals. Instantaneous Frequency and the Complex Signal Reasons for the Complex Signal. The Analytic Signal. Calculating the Analytic Signal. Physical Interpretation of the Analytic Signal. The Quadrature Approximation. Instantaneous Frequency. Density of Instantaneous Frequency. The Uncertainty Principle The Uncertainty Principle. Proof of the Uncertainty Principle. The Uncertainty Principle for the Short-Time Fourier Transform. Densities and Characteristic Functions One Dimensional Densities. One Dimensional Characteristic Functions. Two Dimensional Densities. Local Quantities. Relation Between Local and Global Averages. Distribution of a New Variable. Negative Densities. The Need for Time-Frequency Analysis Simple Analytic Examples. Real Signals. Why Spectra Change. Time-Frequency Distributions: Fundamental Ideas Global Averages. Local Average. Time and Frequency Shift Invariance. Linear Scaling. Weak and Strong Finite Support. Uncertainty Principle. The Uncertainty Principle and Joint Distributions. Uncertainty Principle and Conditional Standard Deviation. The Basic Problems and Brief Historical Perspective. The Short-Time Fourier Transform The Short-Time Fourier Transform and Spectrogram. General Properties. Global Quantities. Local Averages. Narrowing and Broadening the Window. Group Delay. Examples. Inversion. Expansion in Instantaneous Frequency. Optimal Window. The Wigner Distribution Local Averages. Examples. The Wigner Distribution of the Sum of Itoo Signals. Additional Properties. Pseudo Wigner Distribution. Modified Wigner Distributions and Positivity. Comparison of the Wigner Distribution with the Spectrogram. General Approach and the Kernel Method General Class. The Kernel Method. Basic Properties Related to the Kernel. Global Averages. Local Averages. Transformation Between Distributions. Characteristic Function Operator Method Characteristic Function Method. Evaluation of the Characteristic Function. The General Qass. Averages. The Moment Method. Kernel Design for Reduced Interference Reduced Interference Distributions. Kernel Design for Product Kernels. Projection Onto Convex Sets. Baraniuk-Jones Optimal Kernel Design. Some Distributions Choi-Williams Method. Zhao-Atlas-Marks Distribution. Bom-Jordan Distribution. Complex Energy Spectrum. Running Spectrum. Further Developments Instantaneous Bandwidth. Multicomponent Signals. Spatial / Spatial-Frequency Distributions. Delta Function Distribution for FM Signals. Gabor Representation and Time-Frequency Distributions. Expansion in Spectrograms. Spectrogram in Terms of Other Distributions. Singular Value Decomposition of Distributions. Synthesis. Random Signals. Numerical Computation. Signal Analysis and Quantum Mechanics. Positive Distributions Satisfying the Marginals Positive Distributions. The Method of Loughlin, Pitton, and Atlas. The Representation of Signals Orthogonal Expansion of Signals. Operator Algebra. Averages. The Uncertainty Principle for Arbitrary Variables. Density of a Single Variable Density of a Single Variable. Mean Values. Bandwidth. Arbitrary Starting Representation. Joint Representations for Arbitrary Variables Marginals. Characteristic Function Operator Method. Methods of Evaluation. General Class for Arbitrary Variables. Transformation Between Distributions. Local Autocorrelation. Instantaneous Values. Local Values for Arbitrary Variable Pairs. The Covariance. Generalization of the Short-Time Fourier Transform. Unitary Transformation. Inverse Frequency. Appendix. Scale The Scale and Compression Operator. The Scale Eigenfunctions. The Scale Transform. Signals with High Scale Content. Scale Characteristic Function. Mean Scale and Bandwidth. Instantaneous Scale. Uncertainty Principle for Scale. Frequency and Other Scaling. Appendix. Joint Scale Representations Joint Time-Scale Representations. General Class of Time-Scale Representations. Joint Frequency-Scale Representations. Joint Representations of Time, Frequency, and Scale. Appendix. Bibliography Index

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cohen l time frequency analysis theory applications 1995

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