Transform lowpass IIR filter to highpass filter
[num,den] = iirlp2hp(b,a,wc,wd)
[num,den] = iirlp2hp(b,a,wc,wd) with
numerator and denominator coefficients (zeros and poles) for a lowpass
iirlp2bp transforms the magnitude response
from lowpass to highpass.
the coefficients for the transformed highpass filter. For
enter a selected frequency from your lowpass filter. You use the chosen
frequency to define the magnitude response value you want in the highpass
filter. Enter one frequency for the highpass filter — the value
that defines the location of the transformed point — in
Note that all frequencies are normalized between zero and one. Notice
also that the filter order does not change when you transform to a
When you select
wc and designate
the transformation algorithm sets the magnitude response at the
of your bandstop filter to be the same as the magnitude response of
your lowpass filter at
wc. Filter performance between
the values in
wd is not specified, except that
the stopband retains the ripple nature of your original lowpass filter
and the magnitude response in the stopband is equal to the peak response
of your lowpass filter. To accurately specify the filter magnitude
response across the stopband of your bandpass filter, use a frequency
value from within the stopband of your lowpass filter as
Then your bandstop filter response is the same magnitude and ripple
as your lowpass filter stopband magnitude and ripple.
The fact that the transformation retains the shape of the original filter is what makes this function useful. If you have a lowpass filter whose characteristics, such as rolloff or passband ripple, particularly meet your needs, the transformation function lets you create a new filter with the same characteristic performance features, but in a highpass version. Without designing the highpass filter from the beginning.
In some cases transforming your filter may cause numerical problems,
resulting in incorrect conversion to the highpass filter. Use
fvtool to verify the response of your
This example transforms an IIR filter from lowpass to highpass by moving the magnitude response at one frequency in the source filter to a new location in the transformed filter.
Generate a least P-norm optimal IIR lowpass filter with varying attenuation levels in the stopband. Specify a numerator order of 10 and a denominator order of 6. Visualize the magnitude response of the filter.
[b,a] = iirlpnorm(10,6,[0 0.0175 0.02 0.0215 0.025 1], ... [0 0.0175 0.02 0.0215 0.025 1],[1 1 0 0 0 0], ... [1 1 1 1 20 20]); fvtool(b,a)
To generate a highpass filter whose passband flattens out at 0.4π rad/sample, select the frequency in the lowpass filter at 0.0175π, the frequency where the passband starts to roll off, and move it to the new location. Compare the magnitude responses of the filters using FVTool.
wc = 0.0175; wd = 0.4; [num,den] = iirlp2hp(b,a,wc,wd); hvft = fvtool(b,a,num,den); legend(hvft,'Prototype','Target')
The transition band for the highpass filter is essentially the mirror image of the transition for the lowpass filter from 0.0175π to 0.025π, stretched out over a wider frequency range. In the passbands, the filter share common ripple characteristics and magnitude.
 Mitra, Sanjit K., Digital Signal Processing. A Computer-Based Approach, Second Edition, McGraw-Hill, 2001.