# integfrac3D.m

E. Koenig, 08/04/2010

Pseudo-fractional integration of a 3D scale invariant field.

This operation preserves the scale invariance of the initial 3D field. It is realized by a low-pass filter in 1/k^H in the Fourier domain. The value at k=0 is set to the minimum k value which is not null.

The initial field is scale invariant and characterized by

and is very rough, intermittent.

The pseudo-fractional integration will create a smoother version of the initial field. This new field is still scale invariant and characterized by

## Contents

- Use
- Inputs
- Outputs

## Use

y = integfrac3D(x, H, S);

## Inputs

- x: input 3D field
- H: parameter of the low-pass filter.
- S: size of the initial filed.

## Outputs

- y: integrated 3D field.