Design FIR filter with half zero coefficions I noticed a lot of hardware IC use special FIR filters with half zero of coefficients to minimize multiplication operations, especially in decimators/interpolators. E.g.
[ 6 0 -19 0 47 0 -100 0 192 0 -342 0 572 0 -914 0 1409 0 -2119 0 3152 0 -4729 0 7420 0 -13334 0 41527 65536 41527 0 -13334 0 7420  0 -4729 0 3152 0 -2119 0 1409 0 -914 0 572 0 -342 0 192 0 -100 0 47 0 -19 0 6]
or
[-12 0 84 0 -336 0 1006 0 -2691 0 10141 16384 10141 0 -2691 0 1006 0 -336 0 84 0 -12]
I took these coefficients from IC datasheet. I see the center coefficient is 0.5 and other odd coefficients are zero. It effectively halves the mul operations.
But I can't find what the type of the FIR filter is. Is there any good paper? How to create a filter with desired number of taps with this feature?
Oh, these are &quot;Nyquist (M) filters&quot;, in your case M=2. You'll very often find them in mutlirate systems, especially as L-th-band-filters (i.e. filters that only let through 1/L of the Nyquist bandwidth) in decimators.
This is very fundamental for multirate systems, not really &quot;research paper stuff&quot;, so your best bet is hence a good book on Multirate Systems. Fliege has written a classic &quot;Multirate Digital Signal Processing&quot;, harris did, too, with &quot;Multirate Signal Processing For Communication Systems&quot; and Vaidyanathan seems to have written a popular book called &quot;Multirate Systems and Filter Banks&quot;, but I haven't ever read that.