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
representations as inputs to a classifier. You can specify the duration of translation
invariance and the number of wavelet filters per octave.

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.

- Wavelet Scattering
- Music Genre Classification Using Wavelet Time Scattering
- Wavelet Time Scattering for ECG Signal Classification
- Wavelet Time Scattering Classification of Phonocardiogram Data
- Wavelet Time Scattering with GPU Acceleration — Music Genre Classification
- Wavelet Time Scattering with GPU Acceleration — Spoken Digit Recognition