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