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Discrete Wavelet Analysis

DWT, MODWT, dual-tree wavelet transform, wavelet packets, multisignal 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. 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. 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. Use lifting functions to implement perfect reconstruction filter banks with specific properties.

• Signal Analysis
Decimated and nondecimated 1-D wavelet transforms, 1-D discrete wavelet transform filter bank, 1-D dual-tree transforms, wavelet packets, lifting
• Image Analysis
Decimated and nondecimated 2-D transforms, 2-D dual-tree transforms, 2-D lifting schemes, image fusion, wavelet packet analysis
• 3-D Analysis
Discrete wavelet analysis of volumetric data
• Multisignal Analysis
Multivariate signals, multisignal PCA

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