Wavelet Toolbox

Powerful tools for signal and image analysis, compression, and de-noising

The Wavelet Toolbox provides a comprehensive collection of routines for examining local, multiscale, and nonstationary phenomena. Wavelet methods offer additional insight and performance in any application where Fourier techniques have been used. The Toolbox is useful in many signal processing applications, including speech and audio processing, communications, geophysics, finance, and medicine.

Features

Complete GUI and command line functionality for analysis, synthesis, de-noising, and compression of signals and images
Continuous wavelet transform for multiscale signal analysis
Discrete wavelet transform (DWT), providing analysis and synthesis of signals and images
Multiresolution decomposition and analysis of signals and images
Wide selection of wavelet basis functions, including several boundary correction methods
Wavelet packet transform of signals and images
Entropy-based wavelet packet tree pruning for "best-tree" and "best-level" analysis
De-noising with soft and hard thresholding
Compression (minimum coefficient representation)

Highlights

Advanced Techniques. With wavelet analysis, you can see and explore aspects of data that other signal analysis techniques miss, such as trends, breakdown points, discontinuities in higher derivatives, and self similarity. Because wavelet techniques offer a different view of data than those presented by traditional techniques, wavelet analysis can often compress or de-noise a signal without appreciable degradation, even when you want to preserve both high- and low-frequency components.

De-Noising and Compression. Routines for compression and de-noising are provided for both wavelet and wavelet packet techniques. The compression routines extract the minimum number of wavelet coefficients that represent the signal accurately, which is the first stage of a complete compression system.

Wavelet Families. The toolbox provides the following wavelet families: biorthogonal, Daubechies, Haar, Mexican hat, Meyer, Morlet, and Symlets. You can easily add your own wavelet to the toolbox for use at the command line and the graphical user interface.

Demos and Tutorial. An extensive user's guide introduces wavelet concepts and reinforces them with numerous examples and a complete reference section.

Wavelet-Based De-Noising Preserves Underlying Signal

This GUI example shows the automatic de-noising process with the Wavelet Toolbox.

The objective is to de-noise a Doppler chirp with additive wide-band noise, shown in red.
The first step in the de-noising procedure involves decomposing the signal into its original wavelet coefficients. Here, a Symlet wavelet is used to perform a five-level discrete wavelet decomposition.
The second step requires setting all coefficients below a threshold to zero and reconstructing the signal using the inverse wavelet transform. The resulting reconstructed de-noised signal is shown superimposed in yellow.

In this example, the detail coefficients of the wavelet decomposition are shown at each level. The threshold at each level is automatically selected assuming an unscaled white-noise model for optimal de-noising.

Stefan Steinhaus, webmaster@steinhaus-net.de