As many of you know, Hilbert pairs are often constructed by using an odd-
length FIR filter with antisymmetrical coefficients. The I part is taken
from the middle of the delay line and the Q from the output of the
filter.

If you use a Parks/McClellan method for the filter, you will have
coefficients for each tap of the filter.

If you use a window approach instead, The coefficients are 0 for every
other value, so in principle, you need about 1/2 the MACs since half the
MACs are 0.

Assuming a Window approach:

If the length of the filter is 4i-1, that is 3,7,11,..... there will be
2i nonzero coefficients and 2i-1 zero coefficients. The sequence is
w0,0,w2,0,......w(4i-2)

If the length of the filter is 4i+1, that is 5,9,13,..... there will be
2i nonzero coefficients and 2i+1 zero coefficients. The sequence is 0,
w1, 0, w3,....0

There is the same number of non zero coefficients for 4i-1 and 4i+1
length filters.

I calculated both N=11 and N=13 hilbert filters using a Kaiser Window.
The N=13 had a flatter passband even though the number of non zero
coefficients are the same. Since the end points of the N=13 coefficents
are 0, I could truncate the filter to make it smaller. In essense, I now
have a N=11 filter.

I guess this doesn't make too much sense to me. The coefficients are
different, but I am surprised that the filter actually looks much better.

What am I missing?




--
Al Clark
Danville Signal Processing, Inc.
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