Kirthi Devleker, MathWorks
Wavelet Toolbox™ provides functions and apps for analyzing and synthesizing signals, images, and data that exhibit regular behavior punctuated with abrupt changes. The toolbox includes algorithms for the continuous wavelet transform (CWT), scalograms, and wavelet coherence. It also provides algorithms and visualizations for discrete wavelet analysis, including decimated, nondecimated, dual-tree, and wavelet packet transforms. In addition, you can extend the toolbox algorithms with custom wavelets.
The toolbox lets you analyze how the frequency content of signals changes over time and reveals time-varying patterns common in multiple signals. You can perform multiresolution analysis to extract fine-scale or large-scale features, identify discontinuities, and detect change points or events that are not visible in the raw data. You can also use Wavelet Toolbox to efficiently compress data while maintaining perceptual quality and to denoise signals and images while retaining features that are often smoothed out by other techniques.
Wavelet Toolbox provides apps and functions that enable you to analyze and extract features from images and time series data.
You can use the toolbox to de-noise images and time series data, compress images while maintaining perceptual quality, and detect edges and features with different orientations.
You can also use the toolbox to analyze signal power jointly in time and frequency, detect and localize transients and change points in time-series data, and determine optimal signal representations with matching pursuit.
The continuous wavelet algorithms and apps can be used for reconstructing time and frequency localized approximations to signals; analyzing images in space, frequency, orientation; and identifying coherent time-varying oscillations in two signals. For instance, the arrows in this wavelet coherence plot help determine the relative lag between two signals, and the white dashed line indicates points where coherence estimates are reliable.
The discrete wavelet and the wavelet packet algorithms can also be used for analyzing signal variability and correlation between signals on multiple scales.
The toolbox supports a number of wavelet families. You can extend the wavelet algorithms in the toolbox by incorporating custom wavelets, and you also can design and implement perfect reconstruction filter banks using lifting.
For more information on Wavelet Toolbox, please return to the product page.