# lp2hp

Transform lowpass analog filters to highpass

## Description

`[`

transforms an analog lowpass filter prototype with unity cutoff frequency (1 rad/s)
into a highpass analog filter with cutoff angular frequency `bt`

,`at`

] = lp2hp(`b`

,`a`

,`Wo`

)`Wo`

.
Specify the filter prototype with numerator coefficients `b`

and
denominator coefficients `a`

as row vectors. The input system
must be an analog filter prototype.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

`lp2hp`

transforms analog lowpass filter prototypes with a cutoff
angular frequency of 1 rad/s into highpass filters with a desired cutoff angular
frequency. The transformation is one step in the digital filter design process for the
`butter`

, `cheby1`

, `cheby2`

, and `ellip`

functions.

`lp2hp`

is a highly accurate state-space formulation of the classic
analog filter frequency transformation. If a highpass filter is to have a cutoff angular
frequency *ω*_{0}, the standard
*s*-domain transformation is

$$s=\frac{{\omega}_{0}}{p}.$$

The state-space version of this transformation is:

At = Wo*inv(A); Bt = -Wo*(A\B); Ct = C/A; Dt = D - C/A*B;

See `lp2bp`

for a derivation of the bandpass version of this
transformation.

## Extended Capabilities

## Version History

**Introduced before R2006a**