Wavelet Scattering
Model wavelet scattering network in Simulink
 Library:
DSP System Toolbox / Feature Extractors
Description
The Wavelet Scattering block creates a framework for wavelet time
scattering in the Simulink^{®} environment. Use this block to derive lowvariance features from realvalued
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
Input
— Input signal
vector  matrix
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 1byNchann row vector as Nchann separate channels.
When the input data type is single
, the block performs internal
operations in singleprecision. 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
Output
— Output signal
matrix  3D array
Output signal, returned as a matrix or a 3D array.
For a column vector input, the output dimensions are NpathbyNscat, 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 NpathbyNscatbyNchann, where Nchann is the number of columns in the input.
Data Types: single
 double
Parameters
Signal length (samples)
— Signal length in samples
1024
(default)  positive integer ≥ 16
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
Overlap length (Samples)
— Overlap length in samples
0
(default)  positive integer
Specify the overlap (in samples) between consecutive frames of a signal as a nonnegative integer.
Data Types: double
Specify sample rate
— Specify sample rate
off (default)  on
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
Sample rate (Hz)
— Sample rate
16e3
(default)  positive scalar
Specify the sample rate in Hz as a positive scalar.
Dependencies
To enable this parameter, select the Specify sample rate parameter.
Data Types: double
Invariance scale (samples)
— Scattering transform invariance scale in samples
512
(default)  positive integer
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
Invariance scale (s)
— Scattering transform invariance scale in seconds
0.032
(default)  positive scalar
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 onehalf 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
Quality factors
— Quality factors for scattering filter banks
[8
,1
] (default)  positive integer  vector of monotonically decreasing positive integers
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
Reduce the number of scattering paths
— Optimize scattering transform
off (default)  on
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 3dB bandwidth of the wavelet filter in the (i+1)^{th} filter bank must overlap 0 (DC) plus ½ the 3dB bandwidth of the wavelet filter in the i^{th} filter bank.
If this criterion is not satisfied, the higherorder 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
Oversampling factor
— Oversampling factor
0
(default)  nonnegative integer  Inf
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 log_{2} 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 2^{2}
times as many coefficients for
each scattering path with respect to the critically sampled number.
Data Types: double
Boundary signal extension
— Signal extension method
periodic
(default)  reflection
Specify the signal extension method to apply at the boundary as:
periodic
— Extend signal periodically to length2^ceil(log2(N))
, where N is the signal length.reflection
— Extend signal by reflection to length2^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
Include zerothorder coefficients
— Include zerothorder coefficients
off (default)  on
Specify whether to include the zerothorder coefficients.
Data Types: Boolean
Normalization
— Coefficient normalization
none
(default)  parent
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.
Transform
— Transformation on coefficients
none
(default)  log
Specify the type of transformation to apply to the scattering coefficients as
none
or log
.
Model Examples
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

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
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
This block does not support code generation if the dynamic memory allocation is off. To turn on the dynamic memory allocation, run this command in the MATLAB command prompt.
set_param(gcs,'MATLABDynamicMemAlloc','on')
Version History
Introduced in R2022b
See Also
Functions
waveletScattering
(Wavelet Toolbox)
Topics
 Wavelet Scattering (Wavelet Toolbox)
 Fault Detection Using Wavelet Scattering and Recurrent Deep Networks (Wavelet Toolbox)
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