Synopses & Reviews
The practical, heuristic introduction to time-frequency and wavelet analysis.
- Heuristic approach focuses on numerical implementation and real-world applications
- Presents algorithms found in NI's Signal Processing Toolset and other commercial software
- Gabor expansions, linear time-variant filters, and key wavelet transform concepts
- Bilinear time-frequency representation
- Combining time-frequency and wavelet decomposition
In Introduction to Time-Frequency and Wavelet Transforms, Shie Qian takes a heuristic approach to time-frequency and wavelet analysis, drawing upon the engineer's intuitionnot abstract equations. Qian presents the essence of the subject: the information needed to identify applications, choose approaches, and apply time-frequency and wavelet analysis successfully.
Each chapter starts with introductory background, moves to theoretical derivation, and concludes with practical numerical implementation. All algorithms can be found in commercial software, such as the Signal Processing Toolset from National Instruments, and all examples are available for download at NI's Web site. The book presents multiple real-world applications collected from NI's customersmany published here for the first time. Coverage includes:
- Discrete, period discrete, and orthogonal-like Gabor expansions
- Short-time Fourier transforms
- Fast algorithms for computing dual functions
- Linear time-variant filters
- Fundamental wavelet transform concepts
- Bilinear time-frequency representations, including Wigner-Ville distribution and decomposition
- Cohen's Class and other time-dependent power spectra
- Combining time-frequency and time-scale (wavelet) decomposition
If you've wanted to utilize time-frequency and wavelet analysis, but you've been deterred by highly mathematical treatments, Introduction to Time-Frequency and Wavelet Transforms is the accessible, practical guide you've been searching for.
Synopsis
Introduction to Time-Frequency and Wavelet Transforms takes a heuristic approach to time-frequency and wavelet analysis, drawing upon the engineer's intuition, not abstract equations. Discover how to identify applications, choose approaches, and successfully apply time-frequency and wavelet analysis. Shie Qian presents multiple real-world applications -- many previously unpublished. All algorithms are drawn from commercial software, and all examples are available for download.
About the Author
SHIE QIAN is the leading DSP researcher at National Instruments. He has been working on the theory and applications of time-frequency and wavelet analysis for over ten years, in applications including rotating machinery, communications, radar, seismology, and biomedicine. He was a co-guest editor of IEEE Signal Processing magazine's special issue on Time-Frequency Analysis and is a lead author of Joint Time-Frequency Analysis (Prentice Hall). He holds eight patents.
Table of Contents
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.