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Wavelet Scattering

Model wavelet scattering network in Simulink

  • Library:
  • DSP System Toolbox / Feature Extractors

  • Wavelet Scattering block icon

Description

The Wavelet Scattering block creates a framework for wavelet time scattering in the Simulink® environment. Use this block to derive low-variance features from real-valued data and then use those features in machine learning and deep learning applications. The block uses predefined wavelet filters to compute the scalogram and applies an averaging filter to the scalogram for feature extraction. For more information, see Wavelet Scattering (Wavelet Toolbox). To perform wavelet scattering in MATLAB®, use the waveletScattering (Wavelet Toolbox) function.

The Wavelet Scattering block requires Wavelet Toolbox™.

Ports

Input

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Specify the input signal as a vector or a matrix. The block treats each column in the matrix as a separate channel. For example, the block treats a 1-by-Nchann row vector as Nchann separate channels.

When the input data type is single, the block performs internal operations in single-precision. The input data type determines the precision of the scattering decomposition in the filter banks.

The input frame length does not have to match the signal length specified in the block dialog box. The block uses a buffer to feed the wavelet scattering algorithm with frames of length Signal length (samples). If the input frame size does not match the signal length, the block runs in multirate mode.

Data Types: single | double

Output

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Output signal, returned as a matrix or a 3-D array.

For a column vector input, the output dimensions are Npath-by-Nscat, where Npath is the number of scattering paths and Nscat is the number of scattering coefficients in each path, or the resolution of the scattering coefficients.

For matrix inputs, the output dimensions are Npath-by-Nscat-by-Nchann, where Nchann is the number of columns in the input.

Data Types: single | double

Parameters

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Specify the signal length in samples as a positive integer ≥ 16.

The input frame length does not have to match the signal length. The block uses a buffer to feed the wavelet scattering algorithm with frames of length Signal length. If the input frame size does not match the signal length, the block runs in multirate mode.

Data Types: double

Specify the overlap (in samples) between consecutive frames of a signal as a nonnegative integer.

Data Types: double

Specify the sample rate on the block dialog using the Sample rate (Hz) parameter. If you do not select this check box, the frequencies are in cycles/sample and the Nyquist frequency is ½.

Data Types: Boolean

Specify the sample rate in Hz as a positive scalar.

Dependencies

To enable this parameter, select the Specify sample rate parameter.

Data Types: double

Specify the scattering transform invariance scale in samples as a positive integer. Invariance scale specifies the translation invariance of the scattering transform.

If you do not specify the sample rate, invariance scale is measured in samples. If you specify the sample rate, invariance scale is measured in seconds.

Invariance scale cannot exceed the signal length. If signal length is 1000 samples and you do not specify a sample rate, the maximum value of the invariance scale is 1000 samples.

Dependencies

To enable this parameter, clear the Specify sample rate parameter.

Data Types: double

Specify the scattering transform invariance scale in samples as a positive scalar. Invariance scale specifies the translation invariance of the scattering transform.

If you do not specify the sample rate, invariance scale is measured in samples. If you specify the sample rate, invariance scale is measured in seconds. By default, invariance scale is one-half the signal length.

Invariance scale cannot exceed the signal length. If signal length is 1000 samples and you specify a sample rate of 200 Hz, then the maximum value of the invariance scale is 5.

Dependencies

This parameter appears only when you select the Specify sample rate parameter.

Data Types: double

Specify the quality factors for the scattering filter banks as a positive integer or a vector of monotonically decreasing positive integers. A filter bank quality factor is the number of wavelet filters per octave. Quality factors cannot exceed 32 and must be greater than or equal to 1.

By default, the wavelet scattering network the block creates has two filter banks. The first filter bank has a quality factor of eight wavelets per octave and the second filter bank has a quality factor of 1 wavelet per octave.

Data Types: double

Specify whether to optimize the scattering transform and reduce the number of scattering paths.

When you select this parameter, the algorithm reduces the number of scattering paths to compute based on a bandwidth consideration. The scattering transform excludes scattering paths of order 2 and greater that do not satisfy this criterion:

The center frequency minus ½ the 3-dB bandwidth of the wavelet filter in the (i+1)th filter bank must overlap 0 (DC) plus ½ the 3-dB bandwidth of the wavelet filter in the ith filter bank.

If this criterion is not satisfied, the higher-order path is excluded. Selecting the Reduce the number of scattering paths parameter can significantly reduce the number of scattering paths and computational complexity of the scattering transform for most networks.

Data Types: Boolean

Specify the oversampling factor as a nonnegative integer or Inf.

The oversampling factor specifies the factor by which the number of scattering coefficients per signal increase on a log2 scale. By default, the Oversampling factor is set to 0, which corresponds to critically downsampling the coefficients. To obtain a fully undecimated scattering transform, set Oversampling factor to Inf.

Setting Oversampling factor to a value that results in more coefficients than samples is equivalent to setting Oversampling factor to Inf. Increasing the Oversampling factor significantly increases the computational complexity and memory requirements of the scattering transform.

If you set Oversampling factor to 2, the scattering transform returns 22 times as many coefficients for each scattering path with respect to the critically sampled number.

Data Types: double

Specify the signal extension method to apply at the boundary as:

  • periodic — Extend signal periodically to length 2^ceil(log2(N)), where N is the signal length.

  • reflection — Extend signal by reflection to length 2^ceil(log2(2N)), where N is the signal length.

The signal is extended to match the length of the wavelet filters. The length of the filters are powers of two.

The signal extension method is for internal operations. Results are downsampled back onto the scale of the original signal before being returned.

Scattering coefficients

Specify whether to include the zeroth-order coefficients.

Data Types: Boolean

Specify the type of normalization to apply to the scattering coefficients as none or parent. If specified as parent, scattering coefficients of order greater than 0 are normalized by their parents along the scattering path.

Specify the type of transformation to apply to the scattering coefficients as none or log.

Block Characteristics

Data Types

double | single

Direct Feedthrough

no

Multidimensional Signals

no

Variable-Size Signals

no

Zero-Crossing Detection

no

References

[1] Andén, Joakim, and Stéphane Mallat. “Deep Scattering Spectrum.” IEEE Transactions on Signal Processing 62, no. 16 (August 2014): 4114–28. https://doi.org/10.1109/TSP.2014.2326991.

[2] Mallat, Stéphane. “Group Invariant Scattering.” Communications on Pure and Applied Mathematics 65, no. 10 (October 2012): 1331–98. https://doi.org/10.1002/cpa.21413.

Extended Capabilities

Version History

Introduced in R2022b

See Also

Functions