Key Features

  • Time-frequency analysis using the continuous wavelet transform, wavelet coherence, constant-Q transform, and empirical mode decomposition
  • Wavelet Signal Denoiser app for denoising time-series data
  • Decimated wavelet packet and wavelet transforms, including wavelet leaders for fractal analysis
  • Nondecimated discrete techniques, including dual-tree, stationary wavelet, maximal overlap discrete wavelet, and wavelet packet transforms
  • Signal and image denoising and compression, including matching pursuit
  • Lifting method for constructing custom wavelets

Time-Frequency Analysis

Wavelet Toolbox™ provides functions and apps to perform time-frequency analysis of signals using continuous wavelet transform (CWT), Empirical Mode Decomposition, Wavelet Synchrosqueezing, Constant-Q transform and wavelet coherence. You can analyze how the frequency content of a signal changes over time. You can also reconstruct time-frequency localized approximations of signals or filter out time-localized frequency components. Using wavelet coherence, you can reveal time-varying frequency content common in multiple signals. You can also perform data-adaptive time-frequency analysis of signal using Empirical Mode Decomposition.

For images, continuous wavelet analysis shows how the frequency content of an image varies across the image and helps to reveal patterns in a noisy image.

Analyze signals jointly in time and frequency with the CWT.
Sharpen time-frequency estimates of signals and reconstruct oscillatory modes.
Perform data-adaptive time-frequency analysis of nonlinear and nonstationary processes.
Identify spectral features in EKG signals.
Reveal time-varying patterns common in two signals.
Create, visualize, and use filter banks for continuous wavelet transform.
Perform adaptive time-frequency analysis using nonstationary Gabor frames.

Discrete Wavelet Analysis

Wavelet Toolbox provides functions and apps to analyze signals and images into progressively finer octave bands using decimated (downsampled) and nondecimated wavelet transforms, including the maximal overlap discrete wavelet transform (MODWT). The toolbox also supports wavelet packet transforms that partition the frequency content of signals and images into progressively finer equal-width intervals.

Multiresolution analysis enables you to detect patterns that are not visible in the raw data. For example, you can measure the multiscale correlation between two signals or obtain multiscale variance estimates of signals to detect changepoints. You can also reconstruct signal and image approximations that retain only desired features, and compare the distribution of energy in signals across frequency bands. Use the wavelet packet spectrum to obtain a time-frequency analysis of a signal.

Detect changes in the variance of a signal using the MODWT.
Decompose, denoise, and obtain compact feature vectors with wavelet packet transform.
Detect and isolate abrupt changes and trends in signals simultaneously.
Explore time-frequency characteristics of wavelets and scaling functions.
Characterize local signal regularity using wavelets.
Find edges and anomalies in signals and images with the discrete wavelet transform (DWT).
Compare the dual-tree DWT with the standard DWT.
Approximate 3D MRI images with less than 1% of the original data.

Denoising

Wavelet Toolbox provides apps and functions to denoise signals and images. Wavelet and wavelet packet denoising enables you to retain features in your data that are often removed or smoothed out by other denoising techniques.

The Wavelet Signal Denoiser app lets you visualize and automatically denoise time-series data.

Wavelet Toolbox supports a variety of thresholding strategies you can apply to your data and use to compare results. Noise in a signal is not always uniform in time, so you can apply interval-dependent thresholds to denoise data with nonconstant variance.

You can denoise collections of signals with wavelets by exploiting correlations between individual signals. You can also cluster groups of signals by filtering out unimportant details using sparse wavelet representations.  

Visualize and automatically denoise time-series data.
Denoise images while preserving sharp edges.
Remove noise with nonconstant variance using interval-dependent thresholds.
Denoise signals while keeping transient, abrupt changes.
Denoise multivariate signals by exploiting correlations between the signals at multiple scales.

Compression

Wavelet Toolbox provides apps and functions to compress signals and images. You can compress data by setting perceptually unimportant wavelet and wavelet packet coefficients to zero and reconstructing the data. The toolbox offers the Wavelet Design and Analysis app, which you can use to explore signal and image compression.

Overview of wavelet compression.
Compress images while maintaining good visual quality.
Reduce memory footprint to only 15% of the original signal.

Lifting

Wavelet Toolbox provides support for second-generation wavelets through lifting. Lifting enables you to design perfect reconstruction filter banks with specific properties starting from a simple split of the data. Lifting includes all the first-generation wavelets as a special case, but using lifting you can also obtain wavelet transforms suitable for nonuniformly sampled data where first-generation wavelets are not appropriate.

Lifting also provides a computationally efficient approach for analyzing signal and images at different resolutions or scales.

Design a perfect reconstruction filter bank with specific properties.
Explore a computationally efficient approach for multiresolution analysis of signals and images.
Denoise nonuniformly sampled data using multiscale local polynomial transform (Lifting)