On Sun, Jun 26, 2011 at 11:43:46AM +0200, Jörn Nettingsmeier wrote: > 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.
Right. And 'linear' here means 'without a constant term' - we don't want our system to be a Hilbert transform for example. > *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...) Correct. It it the derivative of the phase response w.r.t. angular frequency (minus that value if your convention is that a delay corresponds to positive time). Group delay actually tells us how the 'envelope' of a signal is modified by nonlinear phase response, something we can easily hear on any 'percussive' signals. Let w = 2 * pi * f Suppose you have some filter that has a non-linear phase response, e.g. P(w) = a * w^2 (radians) The corresponding phase delay is D(w) = P(w) / w = a * w (seconds) The group delay is G(w) = dP(w)/dw = 2 * a * w (seconds) Now if you have a relatively narrowband signal centered at some frequency w1, e.g. a 'ping' with a gentle attack, then it would appear to be delayed by 2 * a * w1, not a * w1, because what we hear as delay is the delay on the envelope, not on the 'cycles'. Ciao, -- FA _______________________________________________ Linux-audio-dev mailing list Linux-audio-dev@lists.linuxaudio.org http://lists.linuxaudio.org/listinfo/linux-audio-dev