Название: MATLAB Wavelet Toolbox User's Guide (R2021a)
Автор: Misiti Michel, Misiti Yves, Oppenheim Georges
Издательство: The MathWorks, Inc.
Год: 2021
Страниц: 1160
Язык: английский
Формат: pdf (true)
Размер: 24.7 MB

Analyze and synthesize signals and images using wavelets.

Wavelet Toolbox provides functions and apps for analyzing and synthesizing signals and images. The toolbox includes algorithms for continuous wavelet analysis, wavelet coherence, synchrosqueezing, and data-adaptive time-frequency analysis. The toolbox also includes apps and functions for decimated and nondecimated discrete wavelet analysis of signals and images, including wavelet packets and dual-tree transforms.

Using continuous wavelet analysis, you can study the way spectral features evolve over time, identify common time-varying patterns in two signals, and perform time-localized filtering. Using discrete wavelet analysis, you can analyze signals and images at different resolutions to detect changepoints, discontinuities, and other events not readily visible in raw data. You can compare signal statistics on multiple scales, and perform fractal analysis of data to reveal hidden patterns.

The Wavelet Toolbox software includes a large number of wavelets that you can use for both continuous and discrete analysis. For discrete analysis, examples include orthogonal wavelets (Daubechies' extremal phase and least asymmetric wavelets) and B-spline biorthogonal wavelets. For continuous analysis, the Wavelet Toolbox software includes Morlet, Meyer, derivative of Gaussian, and Paul wavelets.

The choice of wavelet is dictated by the signal or image characteristics and the nature of the application. If you understand the properties of the analysis and synthesis wavelet, you can choose a wavelet that is optimized for your application. Wavelet families vary in terms of several important properties. Examples include:

- Support of the wavelet in time and frequency and rate of decay.
- Symmetry or antisymmetry of the wavelet. The accompanying perfect reconstruction filters have linear phase.
- Number of vanishing moments. Wavelets with increasing numbers of vanishing moments result in sparse representations for a large class of signals and images.
- Regularity of the wavelet. Smoother wavelets provide sharper frequency resolution. Additionally, iterative algorithms for wavelet construction converge faster.
- Existence of a scaling function, φ.

With Wavelet Toolbox you can obtain a sparse representation of data, useful for denoising or compressing the data while preserving important features. Many toolbox functions support C/C++ code generation for desktop prototyping and embedded system deployment.

Contents:
Acknowledgments.
Wavelets, Scaling Functions, and Conjugate Quadrature Mirror Filters.
Continuous Wavelet Analysis.
Discrete Wavelet Analysis.
Time-Frequency Analysis.
Wavelet Packets.
Denoising, Nonparametric Function Estimation, and Compression.
Matching Pursuit.
Code Generation from MATLAB Support in Wavelet Toolbox.
Special Topics.
Featured Examples — Time-Frequency Analysis.
Featured Examples — Discrete Multiresolution Analysis.
Featured Examples — Denoising and Compression.
Featured Examples — Machine Learning and Deep Learning.
Generating MATLAB Code from Wavelet Toolbox Wavelet Analyzer App.
Wavelet Analyzer App Features Summary.