Discrete Multiresolution Analysis

Discrete wavelet transforms (DWTs), including the maximal overlap discrete wavelet transform (MODWT), analyze signals and images into progressively finer octave bands. This multiresolution analysis enables you to detect patterns that are not visible in the raw data. You can use wavelets to obtain multiscale variance estimates of your signal or measure the multiscale correlation between two signals. You can also reconstruct signal (1-D) and image (2-D) approximations that retain only desired features, and compare the distribution of energy in signals across frequency bands. Shearlets provide sparse approximations of anisotropic features in images. Wavelet packets provide a family of transforms that partition the frequency content of signals and images into progressively finer equal-width intervals.

Use Wavelet Toolbox™ functions to analyze signals and images using decimated (downsampled) and nondecimated wavelet transforms. You can create a DWT filter bank and visualize wavelets and scaling functions in time and frequency. You can also create a filter bank using your own custom filters, and determine whether the filter bank is orthogonal or biorthogonal. You can measure the 3-dB bandwidths of the wavelets and scaling functions. You can also measure the energy concentration of the wavelet and scaling functions in the theoretical DWT passbands. Use multisignal analysis to reveal dependencies across multiple signals. Use shearlets to create directionally sensitive sparse representations of images. Determine the optimal wavelet packet transform for a signal or image. Use the wavelet packet spectrum to obtain a time-frequency analysis of a signal.