We can easily design interpolation filters that obey certain frequency-domain constraints using the Parks-McClellan algorithm. However, it's not immediately clear how to enforce time-domain constraints; in particular, I'm interested in generating Nyquist filters. So if I'm oversampling by a factor of
N, I want the filter to have zero-crossings at
kN, for non-zero integer
k (this ensures that the input samples to my interpolator will appear in the output sequence).
I've seen Harris1 talk about a technique for designing half-band filters, i.e. the special case where
N=2. Is there a general solution for this? (I know that we can easily design filters with the window method, but that doesn't give us the same control.)
 Multirate Signal Processing for Communication Systems, pp. 208-209