# iirlp2xn

Transform IIR lowpass filter to IIR real *N*-point
filter

## Syntax

## Description

`[`

transforms an IIR lowpass filter to an IIR real `num`

,`den`

,`allpassNum`

,`allpassDen`

] =
iirlp2xn(`b`

,`a`

,`wo`

,`wt`

)*N*-point
filter.

The `iirlp2xn`

function returns the numerator and denominator
coefficients of the transformed IIR *N*-point filter. The function
also returns the numerator, `allpassNum`

, and the denominator,
`allpassDen`

, of the
*N*^{th} order allpass mapping filter.
The prototype lowpass filter is specified with the numerator `b`

and the denominator `a`

.

The function transforms a real lowpass prototype filter to an
*N*-point filter by applying an
*N*^{th}-order real lowpass to real
multipoint frequency transformation, where *N* is the number of
features being mapped and is given by the length of the vector
`wo`

. By default, the DC feature is kept at its original
location. For more details, see IIR Lowpass to IIR Real N-Point Filter Transformation.

`[`

allows you to specify an additional parameter, `num`

,`den`

,`allpassNum`

,`allpassDen`

] =
iirlp2xn(`b`

,`a`

,`wo`

,`wt`

,`pass`

)`pass`

as
`'pass'`

or `'stop'`

, which chooses between
using the *“Nyquist Mobility”* and the
*“DC Mobility”*, respectively. In the case of
*“Nyquist Mobility”*, the DC feature is kept at
an original frequency and the Nyquist feature is free to move. In the case of
*“DC Mobility”*, the Nyquist feature stays at
its original location and the DC feature is free to move.

Frequencies must be normalized to be between 0 and 1, with 1 corresponding to half the sample rate.

## Examples

## Input Arguments

## Output Arguments

## More About

## References

[1] Krukowski, A., G.D. Cain, and
I. Kale. “Custom Designed High-Order Frequency Transformations for IIR Filters.” In
*38th Midwest Symposium on Circuits and Systems.
Proceedings*, 1:588–91. Rio de Janeiro, Brazil: IEEE, 1996.

[2] Cain, G.D., A. Krukowski and I. Kale, “High Order Transformations for
Flexible IIR Filter Design,” *VII European Signal Processing Conference
(EUSIPCO'94)*, vol. 3, pp. 1582-1585, Edinburgh, United Kingdom,
September 1994.

## Version History

**Introduced in R2011a**