Weighting a mean with log-magnitude can quickly lead to nonsense. Trivial examples:
- 0dB sine at 100hz, 6dB sine at 200hz --> log centroid is 200hz - -6dB sine at 100hz, 12dB sine at 200hz --> log centroid is 300hz (!) Sanfillipo's adaptive median finding technique is still applicable, but will produce the same result as a power or magnitude version. I apply Occam's razor when making decisions about what metrics correspond most closely to nature. I choose the formula which is mathematically simplest while utilizing operations that make sense for the dimensionality of the operands and do not induce undue discontinuities. Power is simpler to compute than magnitude, log-magnitude is rarely sensible outside of perception modeling, and (unlike zero-crossing techniques) a small change in the signal will always produce a proportionally small change in the metrics. At next opportunity I should post up some code describing how to compute higher moments with the differential brightness estimator. – Evan Balster creator of imitone <http://imitone.com> On Thu, Feb 18, 2016 at 1:00 AM, Ethan Duni <ethan.d...@gmail.com> wrote: > >normalized to fundamental frequency or not > >normalized (so that no pitch detector is needed)? > > Yeah tonal signals open up a whole other can of worms. I'd like to > understand the broadband case first, with relatively simple spectral > statistics that correspond to the clever time-domain estimators discussed > so far in the thread. > > The ideas for time-domain approaches got me thinking about what the > optimal time-domain approach would look like. But of course it depends on > what definition of spectral centroid you use. For the mean of the power > spectrum it seems relatively straightforward to get some tractable > expressions - I guess this is the inspiration for the one based on an > approximate differentiator. But I suspect that mean of the log power > spectrum is more perceptually meaningful. > > E > > On Wed, Feb 17, 2016 at 8:34 PM, robert bristow-johnson < > r...@audioimagination.com> wrote: > >> >> >> ---------------------------- Original Message ---------------------------- >> Subject: Re: [music-dsp] Cheap spectral centroid recipe >> From: "Ethan Duni" <ethan.d...@gmail.com> >> Date: Wed, February 17, 2016 11:21 pm >> To: "A discussion list for music-related DSP" < >> music-dsp@music.columbia.edu> >> -------------------------------------------------------------------------- >> >> >>It's essentially computing a frequency median, >> >>rather than a frequency mean as is the case >> >>with the derivative-power technique described >> >> in my original approach. >> > >> > So I'm wondering, is there any consensus on what is the best measure of >> > central tendency for a music signal spectrum? There's the median vs the >> > mean (vs trimmed means, mode, etc). But what is the right domain in the >> > first place: magnitude spectrum, power spectrum, log power spectrum or >> ??? >> >> normalized to fundamental frequency or not normalized (so that no pitch >> detector is needed)? should identical waveforms at higher pitches have the >> same centroid parameter or a higher centroids? >> >> spectral "brightness" is a multi-dimensional perceptual parameter. you >> can have two tones with the same spectral centroid (however consistent way >> you measure it) and sound very different if the "second moment" or >> "variance" is much different. >> >> >> >> -- >> >> >> r b-j r...@audioimagination.com >> >> >> >> >> "Imagination is more important than knowledge." >> >> _______________________________________________ >> dupswapdrop: music-dsp mailing list >> music-dsp@music.columbia.edu >> https://lists.columbia.edu/mailman/listinfo/music-dsp >> > > > _______________________________________________ > dupswapdrop: music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
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