Overview

MATLAB Wavelet Toolbox software includes a large number of wavelets that you can use for both continuous and discrete analysis. For discrete analysis, examples include ortogonal 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 PHI. For continuous analysis, the Wavelet Toolbox software analytic wavelet-based analysis for select wavelets. Signal Reconstruction from Continuous Wavelet Transform Coefficients illustrates the use of the inverse continuous wavelet transform (CWT) for simulated and real-world signals. Entering waveinfo at the command line displays a survey of the main properties of available wavelet families. For a specific wavelet family, use waveinfo with the wavelet family short name. You can find the wavelet family short names listed in the following table and on the reference page for waveinfo.

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