Time Frequency Analysis: Theory and Applications

Paperback | December 1, 1994

byLeon Cohen

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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.

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From Our Editors

This book brings together the methods that have been developed to study time-varying spectra and presents in simple language the physical and mathematical ideas, their origin and motivation, and the challenges of the field.

From the Publisher

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., speec...

From the Jacket

This book brings together the methods that have been developed to study time-varying spectra and presents in simple language the physical and mathematical ideas, their origin and motivation, and the challenges of the field.

Format:PaperbackDimensions:320 pages, 9 × 7 × 0.8 inPublished:December 1, 1994Publisher:Pearson Education

The following ISBNs are associated with this title:

ISBN - 10:0135945321

ISBN - 13:9780135945322

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Extra Content

Table of Contents



 1. The Time and Frequency Description of Signals.


 2. Instantaneous Frequency and the Complex Signal.


 3. The Uncertainty Principle.


 4. Densities and Characteristic Functions.


 5. The Need for Time-Frequency Analysis.


 6. Time-Frequency Distributions: Fundamental Ideas.


 7. The Short-Time Fourier Transform.


 8. The Wigner Distribution.


 9. General Approach and the Kernel Method.


10. Characteristic Function Operator Method.


11. Kernel Design for Reduced Interference.


12. Some Distributions.


13. Further Developments.


14. Positive Distributions Satisfying the Marginals.


15. The Representation of Signals.


16. Density of a Single Variable.


17. Joint Representations for Arbitrary Variables.


18. Scale.


19. Joint Scale Representations.


Bibliography.


Index.

From Our Editors

This book brings together the methods that have been developed to study time-varying spectra and presents in simple language the physical and mathematical ideas, their origin and motivation, and the challenges of the field.