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 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
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
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
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
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.
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
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.
