- when considering finite duration there is the uncertainty principle, so you always deal with a pack of frequencies rather than one frequency, which makes "latency" dependent on the content of that pack.
- however, using FT[th(t)]=j(FT[h(t)])', one can show that the centroid of time w.r.t. the impulse response equals the centroid of group delay w.r.t. frequency response. (again, if the filter is causal then the centroid is nonnegative). This means if your filter is narrow band than the centroid of group delay gives the latency in that band. If your filter is wide band than I guess you can try evaluating group delay centroid from local frequency bands, but I'm not sure of a theory that supports doing so. xue -----Original Message----- From: music-dsp-boun...@music.columbia.edu [mailto:music-dsp-boun...@music.columbia.edu] On Behalf Of Andreas Beisler Sent: 18 March 2011 14:45 To: music-dsp@music.columbia.edu Subject: Re: [music-dsp] Frequency-dependent latency of a filter I guess I see the whole thing a bit more naive. And without the actual implementation details in mind. Yes, the implementation comprises of a DFT and that means we're dealing with everlasting sinusoids. And that's already a problem. But I see it more like having a signal that his made of finite sinusoidal components of possibly changing frequency, and sending this signal through a filter. None of these components will be present at the output of that filter before they are actually input. That's what causality means for me. The system has a delay, and it is frequency dependent, if we are not dealing with a linear-phase filter. This is the delay I am interested in, and I think groupdelay is not the right measure for that, since it can be negative for a causal filter as you say and this doesn't fit with my view that the filter is causal. I could think of a method to measure it (I didn't implement it and I don't know if it would actually work). But you could i.e. make a linear-phase filterbank with very narrow bands. Each of these bands you feed through that filter. Afterwards you do crosscorrelation of each filtered band with each unfiltered band. This should yield an estimate of the delay. It just seems an awful lot of work to estimate the delay of the filter, doesn't it? Andreas -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
