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.

Get Started:

Machine Learning and Deep Learning with Wavelets

Use wavelet techniques to obtain data representations or features for machine learning and deep learning workflows.

Wavelet Scattering

Derive low-variance features from real-valued time series and image data for use in machine learning and deep learning for classification and regression.

Music Genre Classification Using Wavelet Time Scattering

Wavelet-Based Techniques for Deep Learning

Use cwt to generate the 2D time-frequency maps of time series data, which can be used as inputs with deep convolutional neural networks (CNN).

Classify Time Series Using Wavelet Analysis and Deep Learning

Reference Examples

Use examples to get started with using wavelet-based techniques for machine learning and deep learning.

Digit Classification with Wavelet Scattering

Time-Frequency Analysis

Analyze change in frequency content of a signal and images over time

CWT

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.

Obtain sharper resolution and extract oscillating modes from a signal using wavelet synchrosqueezing. Reconstruct time-frequency localized approximations of signals or filter out time-localized frequency components.

Wavelet Analysis of Financial Data

Constant-Q Transform

Perform adaptive time-frequency analysis using nonstationary Gabor frames with the constant-Q transform (CQT).

Constant-Q nonstationary Gabor transform

Discrete Multi-Resolution Analysis

Use functions and apps to perform multiresolution analysis for signals, images and volumes

Decimated Wavelet and Wavelet Packet Analysis 

Perform decimated discrete wavelet transform (DWT) to analyze signals, images, and 3D Volumes in progressively finer octave bands.

Use wavelet packet transform, that partitions frequency content of signals and images into progressively finer equal-width intervals, to preserve global energy and reconstruct exact features. Overcome shift variance in signals, images and volumes using the dual tree wavelet transform.

1-D wavelet decomposition

Nondecimated Wavelet and Wavelet Packet Analysis

Implement nondecimated wavelet transforms like the stationary wavelet transform (SWT), maximum overlap discrete wavelet transforms (MODWT), and maximum overlap wavelet packet transform. 

Use Signal Multiresolution Analyzer App to analyze to generate and compare multilevel wavelet decompositions of signals.

MODWT using Signal Multiresolution Analyzer App

Data-Adaptive Transforms

Decompose nonlinear or nonstationary processes into intrinsic modes of oscillation using empirical mode of decomposition (EMD)

Perform Hilbert spectral analysis on signals to identify localized features

Empirical mode decomposition

Filter Banks

Use functions to obtain and use common orthogonal and biorthogonal wavelet filters. Design perfect reconstruction filter banks through lifting.

Orthogonal and Biorthogonal Filter Banks

Use orthogonal wavelet filter banks like Daubechies, Coiflet, Haar and others to perform multiresolution analysis and feature detection

Biorthogonal filter banks like biorthogonal spline and reverse spline can be used for data compression

Biorthogonal Scaling Function and Wavelet

Lifting

Use lifting to design perfect reconstruction filter banks with specific properties starting from a simple split of the data

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.

Primal Lifting from Haar

Denoising and Compression

Use functions and apps to denoise and compress signals and images

Denoising

Use wavelet and wavelet packet denoising techniques to retain features that are removed or smoothed by other denoising techniques. 

The Wavelet Signal Denoiser app can be used for visualization and denoising 1-D signals.

Denoise a Signal with the Wavelet Signal Denoiser

Compression

Use wavelet and wavelet packets to compress signals and images by setting unimportant coefficients to zero and reconstructing data.

Two-Dimensional True Compression.

Code Generation

Generate C/C++/CUDA® code and create standalone executables

 

Generate C/C++ Code

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 Code for Signal Denoising

Generate CUDA Code

Use GPU Coder™ to generate optimized CUDA code for functions that support GPU code generation.

Run optimized code on GPUs

Latest Features

Shearlets

Generate sparse representations of images automatically for deep learning and image processing

Time-Frequency Gallery

Examine features and limitations of time-frequency analysis methods

GPU Computing

Accelerate automatic feature extraction using wavelet scattering on GPUs

Machine and Deep Learning Examples

Classify signals using wavelet-derived features with classifiers

C/C++ Code Generation

Automatically generate code for multisignal discrete wavelet analysis using MATLAB Coder

See release notes for details on any of these features and corresponding functions.