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Wavelet time scattering

Use the `waveletScattering`

object to create a network for a
wavelet time scattering decomposition using the Gabor (analytic Morlet) wavelet. The network
uses wavelets and a lowpass scaling function to generate low-variance representations of
real-valued time series data. Wavelet time scattering yields representations insensitive to
translations in the input signal without sacrificing class discriminability. You can use the
representations as inputs to a classifier. You can specify the duration of translation
invariance and the number of wavelet filters per octave. The scattering network also supports
time × channel × batch (T×C×B) inputs.

creates a wavelet
time scattering network with two filter banks. The first filter bank has a quality factor
of eight wavelets per octave. The second filter bank has a quality factor of one wavelet
per octave. By default, `sf`

= waveletScattering`waveletScattering`

assumes a signal input length
of 1024 samples. The scale invariance length is 512 samples. By default,
`waveletScattering`

uses periodic boundary conditions.

creates a network for wavelet scattering, `sf`

= waveletScattering(`Name,Value`

)`sf`

, with properties
specified by one or more `Name,Value`

pair arguments. Properties can be
specified in any order as `Name1,Value1,...,NameN,ValueN`

. Enclose each
property name in quotes.

**Note**

With the exception of `OversamplingFactor`

, after creation you
cannot change a property value of an existing scattering network. For example, if you
have a network `sf`

with a `SignalLength`

of 2000,
you must create a second network `sf2`

for a signal with 2001
samples. You cannot assign a different `SignalLength`

to
`sf`

.

`scatteringTransform` | Wavelet 1-D scattering transform |

`featureMatrix` | Scattering feature matrix |

`log` | Natural logarithm of scattering transform |

`filterbank` | Wavelet time scattering filter banks |

`littlewoodPaleySum` | Littlewood-Paley sum |

`scattergram` | Visualize scattering or scalogram coefficients |

`centerFrequencies` | Wavelet scattering bandpass center frequencies |

`numorders` | Number of scattering orders |

`numfilterbanks` | Number of scattering filter banks |

`numCoefficients` | Number of wavelet scattering coefficients |

`paths` | Scattering network paths |

[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.

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