Wavelet time scattering

Use the `waveletScattering`

object to create a framework for a
wavelet time scattering decomposition using the Gabor (analytic Morlet) wavelet. The framework
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
framework to extract features that can be used in many learning algorithms, such as k-nearest
neighbors (kNN), support vector machines (SVM), and boosted decision trees. You can also use
the features in your own classifiers. You can specify the duration of translation invariance
and the number of wavelet filters per octave.

`sf = waveletScattering`

`sf = waveletScattering(Name,Value)`

creates a framework
for a wavelet time scattering decomposition 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 framework 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.

With the exception of `OversamplingFactor`

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

with a `SignalLength`

of
2000, you must create a second framework `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 |

[1] Andén, J., and S. Mallat. "Deep
Scattering Spectrum." *IEEE Transactions on Signal Processing*. Vol. 62,
Number 16, 2014, pp. 4114–4128.

[2] Mallat, S. "Group Invariant
Scattering." *Communications in Pure and Applied Mathematics*. Vol. 65,
Number 10, 2012, pp. 1331–1398.