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. KEY TOPICS: 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. MARKET: 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.
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.
19. Joint Scale Representations.