## Decompose Signal

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 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.

TransformParametersVisualizationRelated Functions
Decimated discrete wavelet transform
• Specify orthogonal or biorthogonal wavelet

• Specify decomposition level

• Specify boundary mode

At level L, the app inserts 2L 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.

TransformParametersVisualizationRelated 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 2L 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 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.

### Workflow

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Select Signal to AnalyzeDecompose SignalExplore Signal Decomposition