Decompose Signal

Step 2 of 5 in Using Wavelet Signal Analyzer App

When you load a signal into Wavelet Signal Analyzer, the app decomposes the signal using the nondecimated discrete wavelet transform. Wavelet Signal Analyzer supports four types of wavelet decomposition:

Decimated (critically-sampled) discrete wavelet transform
Nondecimated discrete wavelet transform
Decimated (critically-sampled) discrete wavelet packet transform
Nondecimated discrete wavelet packet transform

You can decompose the signal using one of the four transforms by clicking Add on the Analyzer tab and selecting a transform. The app creates the decomposition using default wavelet parameters. To learn how to change the parameters, see Modify Wavelet Parameters.

Wavelet Transforms

Wavelet Signal Analyzer supports decimated and nondecimated discrete wavelet transforms.

Transform	Parameters	Visualization	Related Functions
Decimated discrete wavelet transform	Specify orthogonal or biorthogonal wavelet Specify decomposition level Specify boundary mode	At level L, the app inserts 2^L zeros between the decomposition coefficients.	`wavedec`, `waverec`
Nondecimated discrete wavelet transform	Specify orthogonal wavelet Specify decomposition level Specify boundary mode	For all levels, the app displays the decomposition coefficients, and not the multiresolution analysis. You can time-align the coefficients.	`modwt`, `imodwt`

Wavelet Packet Transforms

Wavelet Signal Analyzer supports decimated and nondecimated discrete wavelet packet transforms.

Transform	Parameters	Visualization	Related Functions
Decimated discrete wavelet packet transform	Specify orthogonal or biorthogonal wavelet Specify decomposition level Specify boundary mode	For each terminal-level node, the app inserts 2^L zeros between the decomposition coefficients.	`dwpt`, `idwpt`
Nondecimated discrete wavelet packet transform	Specify orthogonal wavelet Specify decomposition level	For all terminal-level nodes, the app displays the decomposition coefficients and not the MODWPT details. You can time-align the coefficients.	`modwpt`, `imodwpt`

If a wavelet packet decomposition no more than 32 nodes, Wavelet Signal Analyzer displays all the nodes, ordered by relative energy in descending order. Otherwise, the app displays only the top 32 nodes. For more information, see Visualizing Wavelet Packet Terminal Nodes in Wavelet Signal Analyzer.

Modify Wavelet Parameters

To modify the wavelet parameters the app uses to generate a decomposition, open the Wavelet tab and select the decomposition in the Scenarios pane. The app disables the parameters that are not relevant to the decomposition type. Changing any parameter enables the Analyze button.

Wavelet — Specify the wavelet family. For nondecimated transforms, you choose from a list of orthogonal wavelet families. For decimated transforms, you choose from a list of orthogonal and biorthogonal wavelet families.
Number — Specify the wavelet filter number.
Level — Specify the wavelet decomposition level. The length of the signal determines the maximum decomposition level.
Boundary — Depending on the decomposition type, you can specify either periodic or reflection boundary handling.
Time Align — For nondecimated transforms, you can circularly shift the wavelet coefficients at all levels and the scaling coefficients to correct for the delay of the scaling and wavelet filters. For more information, see alignflag.

Note
The app uses time-aligned coefficients only when visualizing the decomposition. It always uses the original coefficients when reconstructing a signal and thresholded original coefficients when compressing signals.

View of toolstrip on Wavelet tab. Use the drop-down lists to choose the wavelet family, wavelet filter number, and boundary condition. Use the spin box to set the decomposition level. For nondecimated decompositions, select the Time Align check box.