FIR facts: True or False.

Stephan M. Bernsee <spam@dspdimension.com> wrote in message news:<2s7qidF1i1aqcU1@uni-berlin.de>...
> On 2004-10-02 15:30:12 +0200, Jerry Avins <jya@ieee.org> said:
> 
> > I was under the impression that ccnvolution was convolution, no matter
> > how implemented; that implemention via FFT/IFFT and via transversal
> > methods produce the same result. Was I wrong?
> > 
> > Jerry
> 
> The DFT produces circular convolution while plain FIRs produce the 
> linear flavor. So, yes and no - the result *can* be the same if you 
> take this into account.

We are back to that 'periodic/non-periodic' thing with the DFT.
A FIR filter implemented in time domain, works on a finite section of 
a discrete-time sequence of infinite duration. End transients are 
appended to this section.

In frequency domain, the DFT is formally correct for periodic discrete-
time sequences of infinite duration. So instead of a start-up transient 
where the initial registers of the FIR filter are 0, the initial states
of the registers are the tail samples of x, because of the signal being
extended periodically. Which is why one needs to zero-pad M-1 samples
to x before transforming to frequency domain.

Rune

On 2004-10-04 08:06:36 +0200, allnor@tele.ntnu.no (Rune Allnor) said:

> We are back to that 'periodic/non-periodic' thing with the DFT.
> A FIR filter implemented in time domain, works on a finite section of a 
> discrete-time sequence of infinite duration. End transients are 
> appended to this section.
> 
> In frequency domain, the DFT is formally correct for periodic discrete-
> time sequences of infinite duration. So instead of a start-up transient 
> where the initial registers of the FIR filter are 0, the initial states
> of the registers are the tail samples of x, because of the signal being
> extended periodically. Which is why one needs to zero-pad M-1 samples
> to x before transforming to frequency domain.
> 
> Rune

Wasn't that what I said? :-)
-- 
Stephan M. Bernsee
http://www.dspdimension.com

Stephan M. Bernsee <spam@dspdimension.com> wrote in message news:<2sc8a6F1ib1cdU1@uni-berlin.de>...
> On 2004-10-04 08:06:36 +0200, allnor@tele.ntnu.no (Rune Allnor) said:
> 
> > We are back to that 'periodic/non-periodic' thing with the DFT.
> > A FIR filter implemented in time domain, works on a finite section of a 
> > discrete-time sequence of infinite duration. End transients are 
> > appended to this section.
> > 
> > In frequency domain, the DFT is formally correct for periodic discrete-
> > time sequences of infinite duration. So instead of a start-up transient 
> > where the initial registers of the FIR filter are 0, the initial states
> > of the registers are the tail samples of x, because of the signal being
> > extended periodically. Which is why one needs to zero-pad M-1 samples
> > to x before transforming to frequency domain.
> > 
> > Rune
> 
> Wasn't that what I said? :-)

Yes it was. The only difference was that you condenced the whole 
explanation of my last paragraph into one term, 'circular convolution'. 
I've been in 'instructor mode' that last couple of days, so I have 
this nasty habit of expanding and elaborating on those kinds of terms. 

Sorry.

Rune