🚀 go-pugleaf

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