# filtfilt

Zero-phase digital filtering

## Description

performs zero-phase digital filtering by processing the input data
`y`

= filtfilt(`b`

,`a`

,`x`

)`x`

in both the forward and reverse directions. After
filtering the data in the forward direction, the function matches initial conditions
to minimize startup and ending transients, reverses the filtered sequence, and runs
the reversed sequence back through the filter. The result has these characteristics:

Zero phase distortion

A filter transfer function equal to the squared magnitude of the original filter transfer function

A filter order that is double the order of the filter specified by

`b`

and`a`

`filtfilt`

implements the algorithm proposed by
Gustafsson [1].

Do not use `filtfilt`

with differentiator and Hilbert FIR
filters, because the operation of those filters depends heavily on their phase
response.

zero-phase filters the input data `y`

= filtfilt(`d`

,`x`

)`x`

using a digital filter
`d`

. Use `designfilt`

to generate `d`

based on
frequency-response specifications.

## Examples

## Input Arguments

## Output Arguments

## References

[1] Gustafsson, F.
“Determining the initial states in forward-backward filtering.”
*IEEE ^{®} Transactions on Signal Processing*. Vol. 44, April 1996,
pp. 988–992. https://doi.org/10.1109/78.492552.

[2] Mitra, Sanjit K.
*Digital Signal Processing*. 2nd Ed. New York: McGraw-Hill,
2001.

[3] Oppenheim, Alan V., and Ronald W. Schafer, with John R. Buck.
*Discrete-Time Signal Processing*. 2nd Ed. Upper Saddle River,
NJ: Prentice Hall, 1999.

## Extended Capabilities

## Version History

**Introduced before R2006a**