# waveletScattering

Wavelet time scattering

## Description

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.

## Creation

### Description

creates a wavelet
time scattering network with two filter banks. The first filter bank has a quality (Q)
factor of eight wavelets per octave. The second filter bank has a Q 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`

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

. Enclose each property name in quotes.

**Note**

After you create a scattering network, you can change the value of the OversamplingFactor property. Depending on the precision of the network and the input signal, the value of the Precision property can also change. All other network property values remain fixed.

## Properties

## Object Functions

`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 |

`gather` | Collect scattering network properties into local workspace |

## Examples

## More About

## 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 R2018b**

## See Also

### Functions

### Objects

### Blocks

- Wavelet Scattering (DSP System Toolbox)

### Topics

- Wavelet Scattering
- Wavelet Scattering Invariance Scale and Oversampling
- Wavelet Time Scattering for ECG Signal Classification
- Wavelet Time Scattering Classification of Phonocardiogram Data
- Wavelet Time Scattering with GPU Acceleration — Spoken Digit Recognition
- Deep Learning Code Generation on ARM for Fault Detection Using Wavelet Scattering and Recurrent Neural Networks