Note: This page has been translated by MathWorks. Click here to see

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

Transform lowpass analog filters to highpass

`[bt,at] = lp2hp(b,a,Wo)`

`[At,Bt,Ct,Dt] = lp2hp(A,B,C,D,Wo)`

`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.