Transform lowpass IIR filter to highpass filter
[num,den] = iirlp2hp(b,a,wc,wd)
[G,AllpassNum,AllpassDen] = iirlp2hp(Hd,Wo,Wt)
where Hd is a dfilt object
[num,den] = iirlp2hp(b,a,wc,wd) with input arguments b and a, the numerator and denominator coefficients (zeros and poles) for a lowpass IIR filter, iirlp2bp transforms the magnitude response from lowpass to highpass. num and den return the coefficients for the transformed highpass filter. For wc, 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 wd. Note that all frequencies are normalized between zero and one. Notice also that the filter order does not change when you transform to a highpass filter.
When you select wc and designate wd, the transformation algorithm sets the magnitude response at the wd values 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 wc. 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 converted filter.
[G,AllpassNum,AllpassDen] = iirlp2hp(Hd,Wo,Wt) returns transformed dfilt object G with a highpass magnitude response. The coefficients AllpassNum and AllpassDen represent the allpass mapping filter for mapping the prototype filter frequency Wo and the target frequencies vector Wt. Note that in this syntax Hd is a dfilt object with a lowpass magnitude response.
This example transforms an IIR filter from lowpass to high pass by moving the magnitude response at one frequency in the source filter to a new location in the transformed filter. To generate a highpass filter whose passband flattens out at 0.4, select the frequency in the lowpass filter where the passband starts to rolloff (wc = 0.0175) and move it to the new location at wd = 0.4.
[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 10 10]); wc = 0.0175; wd = 0.4; [num,den] = iirlp2hp(b,a,wc,wd); fvtool(b,a,num,den);
In the figure showing the magnitude responses for the two filters, the transition band for the highpass filter is essentially the mirror image of the transition for the lowpass filter from 0.0175 to 0.025, 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.