mcmahan@netcom.UUCP (Dave Mc Mahan) (12/06/90)
I have done some playing around with FIR filters for various purposes, and
always find something peculiar. FIR filters always have odd tap counts.
Why is that? I have looked in various DSP books, but can find no hint as
to why that fact is true. The books I have looked in, however, always use
odd tap counts. Can somebody give me a good, clear explaination? I'm more
interested in a real explaination rather than pointers to books or
articles, but will try to find the articles if sited.
-dave
--
Dave McMahan mcmahan@netcom.uucp
{apple,amdahl,claris}!netcom!mcmahanhedstrom@sirius.UVic.CA (Brad Hedstrom) (12/06/90)
In article <18193@netcom.UUCP> mcmahan@netcom.UUCP (Dave Mc Mahan) writes: > I have done some playing around with FIR filters for various purposes, and > always find something peculiar. FIR filters always have odd tap counts. > Why is that? I have looked in various DSP books, but can find no hint as > to why that fact is true. The books I have looked in, however, always use > odd tap counts. Can somebody give me a good, clear explaination? I'm more > interested in a real explaination rather than pointers to books or > articles, but will try to find the articles if sited. A.V. Oppenheim and R.W. Schafer, Digital Signal Processing, 1975, pg. 238. "We note that for the case of N [the filter length] odd, the phase shift corresponds to an integer number of samples delay, while for N even, the delay is an integer plus one-half sample." This also assumes linear phase filter (the coefficients are symmetric). _____________________________________________________________________________ Brad Hedstrom, University of Victoria, ECE Dept. Internet: hedstrom@sirius.uvic.ca UUCP: ...!{uw-beaver,ubc-vision}!uvicctr!hedstrom
wilf@sce.carleton.ca (Wilf Leblanc) (12/07/90)
mcmahan@netcom.UUCP (Dave Mc Mahan) writes: >I have done some playing around with FIR filters for various purposes, and >always find something peculiar. FIR filters always have odd tap counts. >Why is that? I have looked in various DSP books, but can find no hint as >to why that fact is true. The books I have looked in, however, always use >odd tap counts. Can somebody give me a good, clear explaination? I'm more >interested in a real explaination rather than pointers to books or >articles, but will try to find the articles if sited. First of all, FIR filters don't always have odd tap counts. Linear phase FIR filters _usually_ have an odd tap count because the group delay is then fixed at (M-1)/2 for an Mth order FIR filter. If M is odd, (M-1)/2 is not an integer, so the delay through the filter is a non integer. i.e. Case I, M = 3, Linear phase FIR filter H(z) = h(0) + h(1)z^-1 + h(0)z^-2 = z^(-1) [ h(0)z + h(0)z^-1 + h(1) ] The group delay is -d arg(H(e^jw))/dw The part inside [ ] is real so the group delay is = 1 a delay of one sample. Case II, M = 2, Linear Phase FIR filter H(z) = h(0) + h(0) z^-1 = z^(-1/2) [ h(0) z^(1/2) + h(0) z^(-1/2)] In this case the group delay is 1/2, a delay of 1/2 sample ? In many cases this delay of 1/2, or (M-1)/2 samples is undesired, thus it is best to use M odd. Compensating for an integer delay is easy, but to compensate for a non-integer delay is more DSP (i.e. another even order FIR). I don't know if this is the only reason to use an odd tap count Linear Phase FIR, but this is why I usually use odd tap counts. > -dave >-- >Dave McMahan mcmahan@netcom.uucp > {apple,amdahl,claris}!netcom!mcmahan -- Wilf LeBlanc Carleton University Internet: wilf@sce.carleton.ca Systems & Computer Eng. UUCP: ...!uunet!mitel!cunews!sce!wilf Ottawa, Ont, Canada, K1S 5B6
grosen@amadeus.ucsb.edu (Mark D. Grosen) (12/08/90)
Another reason to use odd-length FIR filters is that even-length (symmetric) FIR filters always have a zero at omega = pi (ie, 1/2 the sampling rate). This makes them unsuitable for use as highpass filters, but possibly better for low or bandpass filters. Mark D. Grosen ARPA: grosen@amadeus.ucsb.edu Signal Processing Lab / Communications Research Lab ECE Dept. University of California Santa Barbara, CA 93106