Wavelet Toolbox

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 explore how 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.

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.

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Machine Learning and Deep Learning with Wavelets

Derive low-variance features from real-valued time series and image data for use in machine learning and deep learning for classification and regression. Use continuous wavelet analysis to generate the 2-D time-frequency maps of time series data, which can be used as inputs with deep convolutional neural networks (CNN).

Documentation | Examples

Time-Frequency Analysis

Analyze signals, images jointly in time and frequency with the continuous wavelet transform (CWT) using the Wavelet Analyzer App. Use wavelet coherence to reveal common time-varying patterns. Perform adaptive time-frequency analysis using nonstationary Gabor frames with the constant-Q transform (CQT).

Documentation | Examples

Discrete Multiresolution Analysis

Perform decimated discrete wavelet transform (DWT) to analyze signals, images, and 3-D Volumes in progressively finer octave bands. Implement nondecimated wavelet transforms. Decompose nonlinear or nonstationary processes into intrinsic modes of oscillation using techniques.

Documentation | Examples

Filter Banks

Use orthogonal wavelet filter banks like Daubechies, Coiflet, Haar and others to perform multiresolution analysis and feature detection. Design first- and second-generation wavelets using the lifting method. Lifting also provides a computationally efficient approach for analyzing signal and images at different resolutions or scales.

Documentation | Examples

Denoising and Compression

Use wavelet and wavelet packet denoising techniques to retain features that are removed or smoothed by other denoising techniques. The Wavelet Signal Denoiser app lets you visualize and denoise 1-D signals. Use wavelet and wavelet packets to compress signals and images by removing data without affecting perceptual quality.

Documentation | Examples

Acceleration and Deployment

Speed up your code by using GPU and multicore processors for supported functions. Use the MATLAB^® Coder™ to generate standalone ANSI-compliant C/C++ code from Wavelet Toolbox functions that have been enabled to support C/C++ code generation. Generate optimized CUDA code to run on NVIDIA GPUs for supported functions.

Documentation | Examples

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“The algorithms we developed using MATLAB gave the participant back basic control of his arm and hand. By the end of the study, he could grip a bottle, pour out its contents, and set it down, as well as pick up a stir stick and execute a stirring motion.”
David Friedenberg, Battelle

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