# Determine poles and zeros of a specific filter design

I have a design question and need to determine poles-zeros of a IIR bandpass filter. Requirements are:

1-order should be 3

2-causal

3-real valued impulse response

4-stable

5-cutoff freq: pi/3-pi/2

I have tried butterworth design on matlab to determine poles and zeros but I do want to learn how are they placed analytically or by inspection. Also a problem of matlab is it designed a filter with order=4. Is it possible to solve this with n=3.

Thanks

• @Hilmar: In the first line of the question it says "bandpass". – Matt L. Dec 27 '18 at 18:19

So a reasonable choice would be to place a complex conjugate pole pair at (or close to) the center frequency of the band pass filter, and leave the remaining real-valued pole at $$z=0$$ (where it doesn't affect the magnitude response). The three zeros should all be placed on the unit circle to create frequency response zeros. A reasonable choice would be to have one zero at DC and a complex pair of zeros close to Nyquist.