[LAD] Determining Phase

[Jörn Nettingsmeier]

On 06/26/2011 04:17 AM, Fons Adriaensen wrote:
> On Sun, Jun 26, 2011 at 12:22:58AM +0200, Jörn Nettingsmeier wrote:

> - Phase is related to delay but it is not the same thing.
> Group delay is again something different. Mixing up all
> these is not going to help anyone understand things any
> better.

well, i was trying to connect all those buzzwords... but you are right, 
it should be done more carefully. let me try again.

*delay* makes the *phase* response curve steeper. it doesn't introduce 
any non-linearities in the phase response.

amplitude response over frequency can be interpreted "as-is", but phase 
response needs to be looked at with your first-derivative glasses on: a 
system comprising a perfect speaker and your perfect ear only has zero 
phase when you stick your head into the speaker.
as soon as you move away, the phase drops, the steeper the further you go.
morale: constant amplitude response is what we want. constant phase 
response almost never happens, because of delays that creep in. instead, 
we want _linear_ phase response.

*group* *delay* is a *time* *delay* for a specific frequency. if you 
have a linear-phase system, the group delay is a _constant_: high 
frequencies may be phase-shifted by more cycles, but the time it takes 
them to arrive is the same as for low frequencies.
i think you get the group delay when you differentiate the phase 
response wrt frequency (but don't believe me when i talk calculus...)

it's important not to confuse phase delay with group delay: phase delay 
talks about a number of cycles of delay, whereas group delay is about 
time. when you want to assess how well a system responds to transients, 
you don't care how often the high frequencies have been wiggling around 
on the way to your ear drum - you want them to arrive at the same time 
as the low frequencies. hence, you care about the group delay, not the 
phase delay.