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 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 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).

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

Continuous Wavelet Transform

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 Multiresolution 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 3-D Volumes in progressively finer octave bands.

Use wavelet packet transforms to partition the frequency content of signals and images into progressively narrower equal-width intervals while preserving the overall energy of the data. Use dual-tree wavelet transforms to obtain shift-invariant, minimally redundant discrete wavelet analyses of signals and images.

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 the Signal Multiresolution Analyzer App to generate and compare multilevel wavelet or empirical mode decompositions of signals. 

MODWT using Signal Multiresolution Analyzer App

Data-Adaptive Transforms

Decompose nonlinear or nonstationary processes into intrinsic modes of oscillation using techniques like empirical mode decomposition (EMD) and variational mode decomposition (VMD).

Perform Hilbert spectral analysis on signals to identify localized features.

Variational 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

Lifting also provides a computationally efficient approach for implementing the discrete wavelet transform on signals or images.

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 removing data without affecting perceptual quality.

Two-Dimensional True Compression.

Acceleration and Deployment

Generate C/C++ and CUDA® code and MEX functions, and run functions on a graphics processing unit (GPU)

 

Accelerating Your Code

Speed up your code by using GPU and multicore processors for supported functions.

Spoken Digit Recognition with GPU Acceleration

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 optimized CUDA code to run on NVIDIA GPUs for supported functions.

Generate Code for Signal Denoising

Latest Features

Time-Frequency Analysis

Use variational mode decomposition to extract intrinsic modes

Kingsbury Q-shift Dual-Tree Complex Wavelet Transforms

Perform shift-invariant and directionally sensitive discrete multiresolution analysis with minimal redundancy

1-D Multisignal Discrete Wavelet Packet Transforms

Automatically perform wavelet packet analysis of multichannel signals

New Examples

Hands-on introductions to continuous wavelet analysis and multiresolution analysis

wcoherence Function

Compute wavelet coherence over user-specified frequency or period range

GPU Computing

Accelerate continuous wavelet transform and Wigner-Ville distribution

GPU Code Generation

Generate single precision code for cwt

C/C++ Code Generation:

Automatically generate code for discrete wavelet analysis, time-frequency analysis, denoising, multiscale variance estimation and single precision code for cwtfilterbank

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