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.

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.

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.  

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.

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.