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:
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
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
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
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
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.
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
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.
