Introduction to Time-Frequency and Wavelet Transforms

1. Introduction. 2. Fourier Transform A Mathematical Prism. Frame. Fourier Transform. Relationship between Time and Frequency Representations. Characterization of Time Waveform and Power Spectrum. Uncertainty Principle. Discrete Poisson-Sum Formula. Short-Time Fourier Transform and Gabor Expansion. 3. Short-Time Fourier Transform. Gabor Expansion. Periodic Discrete Gabor Expansion. Orthogonal-Like Gabor Expansion. A Fast Algorithm for Computing Dual Functions. Discrete Gabor Expansion. 4. Linear Time-Variant Filters. LMSE Method. Iterative Method. Selection of Window Functions. 5. Fundamentals of theWavelet Transform. Continuous Wavelet Transform. Piecewise Approximation. Multiresolution Analysis. Wavelet Transformation and Digital Filter Banks. Applications of the Wavelet Transform. 6. Digital Filter Banks andtheWavelet Transform. Two-Channel Perfect Reconstruction Filter Banks. Orthogonal Filter Banks. General Tree-Structure Filter Banks and Wavelet Packets. 7. Wigner-Ville Distribution. Wigner-Ville Distribution. General Properties of the Wigner-Ville Distribution. Wigner-Ville Distribution for the Sum of Multiple Signals. Smoothed Wigner-Ville Distribution. Wigner-Ville Distribution of Analytic Signals. Discrete Wigner-Ville Distribution. 8. Other Time-Dependent Power Spectra. Ambiguity Function. Cohens Class. Some Members of Cohens Class. Reassignment. 9. Decomposition of the Wigner-Ville Distribution. Decomposition of the Wigner-Ville Distribution. Time-Frequency Distribution Series. Selection of Dual Functions. Mean Instantaneous Frequency and Instantaneous Bandwidth. Application for Earthquake Engineering. 10. Adaptive Gabor Expansion and Matching Pursuit. Matching Pursuit. Adaptive Gabor Expansion. Fast Refinement. Applications of the Adaptive Gabor Expansion. Adaptive Gaussian Chirplet Decomposition. Optimal Dual Functions. Bibliography. Index.