Jörn Nettingsmeier nettings at folkwang-hochschule.de
Sun Jun 26 09:43:46 UTC 2011

```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
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.

```