Re: outstanding changesets

[Daniel J Sebald]

Ben Abbott wrote:
> On Feb 1, 2009, at 1:56 PM, Daniel J Sebald wrote:
>
> > Ben Abbott wrote:
> >
> > > On Jan 29, 2009, at 1:50 AM, Søren Hauberg wrote:
> > >
> > > > ons, 28 01 2009 kl. 22:13 -0500, skrev John W. Eaton:
> > > >
> > > > > Does Matlab produce the same result?
> > > >
> > > >
> > > >
> > > > Matlab produces the attached pdf
> > > >
> > > > Søren
> > > > <matlab_freqz.pdf>
> > >
> > > ? ... that is not what I expected. My impression was the Matlab   
> > > unwrapped the phase in such a way that only positive delays would   
> > > result. However, in this example, it appears to be opposite.
> > > Any idea what they are doing?
> >
> >
> > To "unwrap the phase" does not mean disallowing negative, it means  to 
> > remove any 360 degree jumps from the phase which were created as  a 
> > consequence of the modular arithmetic of phase angles.  Note that  if 
> > there are 180 degree phase shifts, those stay because they are  actual 
> > phase jumps.
> >
> > Dan
>
>
> Hi Dan,
>
> What I've inferred is that Matlab's implementation favors unwrapping  
> the phase so that the phase slope is negative (downward sloping), and  
> the delay is positive.
>
> See the examples at the link below.
>
>     http://hauberg.org/wiki/doku.php?id=freqz
>
> Ben

Yes, negative phase, positive delay assumes a causal system (i.e., something 
happens and then there is a response, not the other way around), but that is 
pretty conventional.  The discrete-time Fourier transform is defined

X(omega) = sum x[n] e^{-j omega n}

such that with x[n] nonzero only for n > 0 (or more generally, a right-sided 
sequence) the minus sign gives negative phase.

Dan