Re: [music-dsp] BW limited peak computation?
TL; DR A high-pass filter? The first and second derivatives could be easily enough described with first and second-order feedback filters, respectively, but once you start fitting that stuff into DSP terminology, then you might as well make a low-order high-pass filter that has the characteristics you desire. If you're looking for the time of the peak, I've had a lot of luck by taking the time (or index) of samples weighted by their values. This produces surprisingly high accuracy. I'm sure very mathy person will tell me why that is mathematically inaccurate, and some other mathy person will probably tell them that it is approximately correct to some precision criteria... On Jul 25, 2016 2:01 PM, "Paul Stoffregen" wrote: > Does anyone have any suggestions or references for an efficient algorithm > to find the peak of a bandwidth limited signal? > > If I just look only at the numerical values of the samples (yeah, that's > what I've been doing), when a signal is close to an integer division of Fs, > even collecting data over many cycles tends to miss the phases of the > waveform containing the peaks. For example: > > Image also available here: https://forum.pjrc.com/threads > /35478-Problems-Plotting-Filter-Response?p=110442&viewfull=1#post110442 > > The only solution I'm imagining would involve expensive upsampling and > filtering. Even then, if I multiply the sample rate by 16 or more and the > filter is good enough, I still might not get a sample right at the peak. > > Is there a better way? > > ___ > 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
Re: [music-dsp] BW limited peak computation?
Hi, I missed this thread until now. Last year, I published an article on this topic here: https://techblog.izotope.com/2015/08/24/true-peak-detection/ In it is included a proof that the true peak can be unboundedly higher than the sample peak. Thanks, -Russell On Mon, Aug 1, 2016 at 5:05 PM, Theo Verelst wrote: > Paul Stoffregen wrote: >> >> Does anyone have any suggestions or references for an efficient algorithm >> to find the peak >> of a bandwidth limited signal? >> > > Hi, > > I think without getting lost in quadratic algebra or endless searches for a > holy grail that doesn't exist that I don't take part in, you've answered the > main theoretical question yourself: to know the signal between the samples, > you need perfect reconstruction to the actual signal, and then analyze that. > > Of course, like the "Fast Lookahead Limiter" from Ladspa or LV2 which I use > regularly does, you could up-sample to a reasonably high sampling frequency > with the best tools you've got, and hope the best of a tool that up-samples > another 8 times (IIRC) and leave it at it that if you're using decent input > signals to your sampling path that there aren't a great many signals > actually mirrors around the Nyquist frequency so that a tool like that will > doe a reasonable flattening job. > > Of course it's possible there's one peak in your signal at 1/4*PI between > two samples such that no matter what a rational fraction between samples you > compute you could never find it with infinite accuracy... I suppose however > in most practical cases you can have a pre-conditioned situation where you > know which possible up-samplers are going to be used on your decent digital > signal product, like wide window sinc, standard short interpolation and a > couple of other methods (FIR/IIR approximations, wave shape approximations, > multi-band approaches, and for the pro's: average based frequency components > with multi-limited computations in the 96kHz or higher sampling domain). If > you know what the customers are going to use as up-sampler, and once with > the final product you make a reasonable quality wide-window sync up-sampled > test run to see if there are any special cases to tend to, you could work > with that, unless people enjoy endless (but not particularly useful) > discussions on heuristics. > > Theo V. > > ___ > 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
Re: [music-dsp] BW limited peak computation?
Paul Stoffregen wrote: Does anyone have any suggestions or references for an efficient algorithm to find the peak of a bandwidth limited signal? Hi, I think without getting lost in quadratic algebra or endless searches for a holy grail that doesn't exist that I don't take part in, you've answered the main theoretical question yourself: to know the signal between the samples, you need perfect reconstruction to the actual signal, and then analyze that. Of course, like the "Fast Lookahead Limiter" from Ladspa or LV2 which I use regularly does, you could up-sample to a reasonably high sampling frequency with the best tools you've got, and hope the best of a tool that up-samples another 8 times (IIRC) and leave it at it that if you're using decent input signals to your sampling path that there aren't a great many signals actually mirrors around the Nyquist frequency so that a tool like that will doe a reasonable flattening job. Of course it's possible there's one peak in your signal at 1/4*PI between two samples such that no matter what a rational fraction between samples you compute you could never find it with infinite accuracy... I suppose however in most practical cases you can have a pre-conditioned situation where you know which possible up-samplers are going to be used on your decent digital signal product, like wide window sinc, standard short interpolation and a couple of other methods (FIR/IIR approximations, wave shape approximations, multi-band approaches, and for the pro's: average based frequency components with multi-limited computations in the 96kHz or higher sampling domain). If you know what the customers are going to use as up-sampler, and once with the final product you make a reasonable quality wide-window sync up-sampled test run to see if there are any special cases to tend to, you could work with that, unless people enjoy endless (but not particularly useful) discussions on heuristics. Theo V. ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] BW limited peak computation?
2016-07-29 9:44 GMT+02:00 Stefano D'Angelo : > 2016-07-29 8:55 GMT+02:00 : >> >> On Jul 25, 2016, at 3:20 PM, Stefano D'Angelo wrote: >> >>> Otherwise, you might very well use higher-order (i.e., not just >>> linear) interpolators, (e.g., not-a-knot cubic spline interpolator), >> >> What is a "not-a-knot cubic spline interpolator"? >> Jerry > > Informally speaking, given two points between which to interpolate, > you are left with two degrees of freedom to define a cubic (spline) > interpolating function. Among all the possibilities, if you impose > continuity of the third derivatives between different splines for each > segment (as you go through samples), what you get are so-called > "not-a-knot" splines. Sorry, I mean, you impose continuity of first and second derivatives between segments, and continuity of third derivative at the second point and at the point just before the last one. (This is how the MATLAB spline function works by default, IIRC). -- Stefano D'Angelo http://sdangelo.github.io/ ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] BW limited peak computation?
2016-07-29 8:55 GMT+02:00 : > > On Jul 25, 2016, at 3:20 PM, Stefano D'Angelo wrote: > >> Otherwise, you might very well use higher-order (i.e., not just >> linear) interpolators, (e.g., not-a-knot cubic spline interpolator), > > What is a "not-a-knot cubic spline interpolator"? > Jerry Informally speaking, given two points between which to interpolate, you are left with two degrees of freedom to define a cubic (spline) interpolating function. Among all the possibilities, if you impose continuity of the third derivatives between different splines for each segment (as you go through samples), what you get are so-called "not-a-knot" splines. Best, -- Stefano D'Angelo http://sdangelo.github.io/ ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] BW limited peak computation?
On Jul 25, 2016, at 3:20 PM, Stefano D'Angelo wrote: > Otherwise, you might very well use higher-order (i.e., not just > linear) interpolators, (e.g., not-a-knot cubic spline interpolator), What is a "not-a-knot cubic spline interpolator"? Jerry ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] BW limited peak computation?
> Because I don't think there can be more than one between any two
> adjacent sampling times.
>
>
> This really got the gears turning. It seems true, but is it a theorem?
> If not, can anyone give a counterexample?
>
I don't know whether it's a classical theorem, but I think it is true.
Yeah, I thought it was true too, but figured out some counterexamples last
night.
The simplest counterexample is two superimposed sincs which have been
shifted apart just far enough that the main hump gets a cleft in it. For
example, try plotting y(t)=sinc(t+0.175)+sinc(t-1.175), where the sinc is
normalized as you proposed. This has two maxima between 0 and 1.
You can also start with a sinc function with a cutoff that's well below
Nyquist, say Nyquist/10. Take a few of these, shift them away from each
other very slightly in time, and multiply them all together. This will
convolve the frequency spectra together, but the result will still be
bandlimited below Nyquist. Any zero of the original sinc is now several
very closely spaced zeros, which means there are also several very closely
spaced extrema. With this procedure you can generate as many local extrema
as you'd like between two samples.
The "wiggles" you get this way tend to be tiny compared to the surrounding
samples, so I think you can safely ignore this sort of thing in practice.
-Ethan
On Thu, Jul 28, 2016 at 12:18 AM, Ross Bencina
wrote:
> On 28/07/2016 12:04 AM, Ethan Fenn wrote:
>
>> Because I don't think there can be more than one between any two
>> adjacent sampling times.
>>
>>
>> This really got the gears turning. It seems true, but is it a theorem?
>> If not, can anyone give a counterexample?
>>
>
> I don't know whether it's a classical theorem, but I think it is true.
>
> Define the normalized sinc function as:
>
> sinc(t) := sin( pi t ) / (pi t)
>
> sinc(0) = 1. the signal is analytic everywhere.
>
> A bandlimited, periodically sampled discrete-time signal {x_n} can be
> interpolated by a series of time-shifted normalized sinc functions, each
> centered at time n and scaled by amplitude x_n. This procedure can be used
> to produce the continuous-time analytic signal x(t) induced by {x_n}. We
> want to know how many peaks (direction changes) there can be in x(t)
> between x(n) and x(n+1).
>
> Sinc is bandlimited and has no frequencies above the Nyquist rate (fs/2).
> A sum of time shifted sincs is also bandlimited and therefore has no
> frequencies above the Nyquist rate.
>
> Now all you need to do is prove that a band-limited analytic signal whose
> highest frequency is fs/2 has no more than one direction change per sample
> period. I can't think how to do that formally right now, but intuitively it
> seems plausible that a signal with no frequencies above the nyquist rate
> would not have time-domain peaks spaced closer than the sampling period.
>
> Ross.
>
>
>
>
> ___
> 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
Re: [music-dsp] BW limited peak computation?
On 28/07/2016 12:04 AM, Ethan Fenn wrote:
Because I don't think there can be more than one between any two
adjacent sampling times.
This really got the gears turning. It seems true, but is it a theorem?
If not, can anyone give a counterexample?
I don't know whether it's a classical theorem, but I think it is true.
Define the normalized sinc function as:
sinc(t) := sin( pi t ) / (pi t)
sinc(0) = 1. the signal is analytic everywhere.
A bandlimited, periodically sampled discrete-time signal {x_n} can be
interpolated by a series of time-shifted normalized sinc functions, each
centered at time n and scaled by amplitude x_n. This procedure can be
used to produce the continuous-time analytic signal x(t) induced by
{x_n}. We want to know how many peaks (direction changes) there can be
in x(t) between x(n) and x(n+1).
Sinc is bandlimited and has no frequencies above the Nyquist rate
(fs/2). A sum of time shifted sincs is also bandlimited and therefore
has no frequencies above the Nyquist rate.
Now all you need to do is prove that a band-limited analytic signal
whose highest frequency is fs/2 has no more than one direction change
per sample period. I can't think how to do that formally right now, but
intuitively it seems plausible that a signal with no frequencies above
the nyquist rate would not have time-domain peaks spaced closer than the
sampling period.
Ross.
___
dupswapdrop: music-dsp mailing list
music-dsp@music.columbia.edu
https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] BW limited peak computation?
> > Because I don't think there can be more than one between any two adjacent > sampling times. This really got the gears turning. It seems true, but is it a theorem? If not, can anyone give a counterexample? Back to the main question... I think you're really going to need to oversample by at least 2x. As Robert's example shows, it's hard to even know where to look for extrema without oversampling. If you want to further refine the extrema after doing this you could try the methods proposed by Stefan or Xue, or try something like a golden section search using the interpolator of your choice. -Ethan On Wed, Jul 27, 2016 at 1:29 AM, robert bristow-johnson < r...@audioimagination.com> wrote: > > > Original Message ---------------- > Subject: Re: [music-dsp] BW limited peak computation? > From: "Ross Bencina" > Date: Tue, July 26, 2016 6:21 pm > To: music-dsp@music.columbia.edu > -- > > > On 27/07/2016 7:09 AM, Sampo Syreeni wrote: > >> Now, what I wonder is, could you still somehow pinpoint the temporal > >> location of an extremum between sampling instants, by baseband logic? > >> Because I don't think there can be more than one between any two > >> adjacent sampling times. > > > > Presumably the certainty of such an estimate would depend on how many > > baseband time samples you considered. Sinc decays as 1/x so that gives > > you some idea of the potential influence of distant values -- not sure > > exactly how that maps into distant sample's influence on peak location > > though. > > > > for normal bandlimited interpolation, i don't think you need to go more > than +16 and -15 samples from the interpolated region (which is between 0 > and 1) and i don't think you'll need to have more than 16 or 32 phases. > and i think you can decently apply quadratic interpolation between those > 1/16th or 1/32nd sample values and you'll have, for all quantitative > purposes, a very good interpolation of the peak. > > dunno what exactly is meant by "baseband logic". > > > -- > > > > > 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
Re: [music-dsp] BW limited peak computation?
Original Message Subject: Re: [music-dsp] BW limited peak computation? From: "Ross Bencina" Date: Tue, July 26, 2016 6:21 pm To: music-dsp@music.columbia.edu -- > On 27/07/2016 7:09 AM, Sampo Syreeni wrote: >> Now, what I wonder is, could you still somehow pinpoint the temporal >> location of an extremum between sampling instants, by baseband logic? >> Because I don't think there can be more than one between any two >> adjacent sampling times. > > Presumably the certainty of such an estimate would depend on how many > baseband time samples you considered. Sinc decays as 1/x so that gives > you some idea of the potential influence of distant values -- not sure > exactly how that maps into distant sample's influence on peak location > though. > for normal bandlimited interpolation, i don't think you need to go more than +16 and -15 samples from the interpolated region (which is between 0 and 1) and i don't think you'll need to have more than 16 or 32 phases. �and i think you can decently apply quadratic interpolation between those 1/16th or 1/32nd sample values and you'll have, for all quantitative purposes, a very good interpolation of the peak. dunno what exactly is meant by "baseband logic". -- � 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
Re: [music-dsp] BW limited peak computation?
On 27/07/2016 7:09 AM, Sampo Syreeni wrote: Now, what I wonder is, could you still somehow pinpoint the temporal location of an extremum between sampling instants, by baseband logic? Because I don't think there can be more than one between any two adjacent sampling times. Presumably the certainty of such an estimate would depend on how many baseband time samples you considered. Sinc decays as 1/x so that gives you some idea of the potential influence of distant values -- not sure exactly how that maps into distant sample's influence on peak location though. Ross. ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] BW limited peak computation?
On 2016-07-26, Stefan Stenzel wrote: the acid test is when the pre-upsampled data is alternating signs on a large amplitude with *one* sample missing. like: ... -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, ... you might get an unnaturally large peak (many times bigger than |A|) with that. Should be something like the sum of all 2A/(pi*(t+0.5)) for t an integer going from zero to infinity. Not sure if that converges. It doesn't. Intuitively speaking, after some heady limit arguments, a pure ...,+1, -1, +1,-1,... train decodes as a sinusoid at the Nyquist frequency. It does so because of phase cancellation between the various, in-phase but at least double in period sinusoids which go into the Nyquist-Shannon reconstruction. What this particular sequence does is, it sums two one-sided alternating sequences together, too. But it does it so that it leaves out a single sample at the origin, and by doing so, pushes those otherwise nicely cancelling, marginal cosines from the various sinc(x) functions into phase between two sampling times. Obviously what you get then is not convergence, but very fast divergence. All within the band-limited interpolation theorem, which in the limit only applies in general strictly below the Nyquist frequency. (This stuff for once doesn't converge even in the weak, distribution sense.) Now, what I wonder is, could you still somehow pinpoint the temporal location of an extremum between sampling instants, by baseband logic? Because I don't think there can be more than one between any two adjacent sampling times. And if you can pinpoint its location, then I believe you could derive an iterative algorithm relying on higher and higher, recursively computed interpolation formulae which could drive the uncertainty in its location as low as necessary. On the fly. Irrespective of what the real *amplitude* of the thing really is. If you could do that, I think you could then put upper bounds on both the L^1 and L^2 norms of the deviation above full range, between the sampling instants, in closed form. And once you'd done that, I think you could pretty much tame any sonically/musically relevant problem happening "between the samples", as well: just take note of where the peak seems to be for phase stuff, and then take note of how rapidly your interpolands grow, for an approximation of what you should do wrt amplitude. -- Sampo Syreeni, aka decoy - de...@iki.fi, http://decoy.iki.fi/front +358-40-3255353, 025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2 ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] BW limited peak computation?
Original Message
Subject: Re: [music-dsp] BW limited peak computation?
From: "Stefan Stenzel"
Date: Tue, July 26, 2016 3:28 pm
To: r...@audioimagination.com
music-dsp@music.columbia.edu
--
>
>> On 26 Jul 2016, at 19:37 , robert bristow-johnson
>> wrote:
>> []
>> the acid test is when the pre-upsampled data is alternating signs on a large
>> amplitude with *one* sample missing. like:
>>
>> ... -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A,
>> +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, ...
>>
>> you might get an unnaturally large peak (many times bigger than |A|) with
>> that.
>
> Should be something like the sum of all 2A/(pi*(t+0.5)) for t an integer
> going from zero to infinity.
> Not sure if that converges.
Stefan, we both know that
�
� �+inf
� �SUM{ �(1/n)^p �}
� �n=0
�
doesn't converge until p gets larger than 1. �(according to Calvin and Hobbes,
instead of the "Big Bang", it's the "Horrendous Space Kablooey".)
�
so the gooder your band-limited interpolation is done, the nastier that
bandlimited
"singularity" (lacking for a better term, maybe "anomaly") gets.
but since the summation is finite, you always get a number, but it might be a
lot bigger than the ostensible amplitude of the signal.
--
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
Re: [music-dsp] BW limited peak computation?
> On 26 Jul 2016, at 19:37 , robert bristow-johnson > wrote: > [] > the acid test is when the pre-upsampled data is alternating signs on a large > amplitude with *one* sample missing. like: > > ... -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, > +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, -A, +A, ... > > you might get an unnaturally large peak (many times bigger than |A|) with > that. Should be something like the sum of all 2A/(pi*(t+0.5)) for t an integer going from zero to infinity. Not sure if that converges. ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] BW limited peak computation?
Original Message Subject: Re: [music-dsp] BW limited peak computation? From: "Stefan Stenzel" Date: Tue, July 26, 2016 12:08 pm To: music-dsp@music.columbia.edu -- > > It all depends what you consider a peak. Imagine a single sample of one, > surrounded by nothing but zeros left and right, upsampling this signal would > bring up many peaks that you might not be interested in. > � my guess would also be upsampling by some factor (say 8 or 16) and picking out the maximum values (and then maybe quadratic interpolation around the discrete but upsampled peak). the upsampling would likely be the ol' polyphase interpolation thing that is common. �maybe 16 or 32 samples in the summation at most the acid test is when the pre-upsampled data is alternating signs on a large amplitude with *one* sample missing. �like: �...�-A, +A,�-A, +A, -A, +A,�-A, +A,�-A, +A,�-A, +A,�-A, +A,�-A, +A,�-A, +A, +A, -A, +A,�-A, +A,�-A, +A,�-A, +A,�-A, +A,�-A, +A,�-A, +A,�-A, +A, ... you might get an unnaturally large peak (many times bigger than |A|) with that. -- 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
Re: [music-dsp] BW limited peak computation?
Paul, It all depends what you consider a peak. Imagine a single sample of one, surrounded by nothing but zeros left and right, upsampling this signal would bring up many peaks that you might not be interested in. For practical purposes I suggest you start with the simple approach to search for a sample with neighbours smaller in magnitude, refine the fractional position of the peak and then evaluate the peak value at this position. A simple quadratic function and its derivative for this: suppose a,b,c are successive samples and b having maximum magnitude: fraction(a,b,c) = (a-c)/(2a-4b+2c) value(a,b,c,fraction) = ((a-2b+c)fraction^2 + (c-a)fraction + 2b)/2 This would work well with the data in your graphs. Stefan > On 25 Jul 2016, at 23:00 , Paul Stoffregen wrote: > > Does anyone have any suggestions or references for an efficient algorithm to > find the peak of a bandwidth limited signal? > > If I just look only at the numerical values of the samples (yeah, that's what > I've been doing), when a signal is close to an integer division of Fs, even > collecting data over many cycles tends to miss the phases of the waveform > containing the peaks. For example: > > > Image also available here: > https://forum.pjrc.com/threads/35478-Problems-Plotting-Filter-Response?p=110442&viewfull=1#post110442 > > The only solution I'm imagining would involve expensive upsampling and > filtering. Even then, if I multiply the sample rate by 16 or more and the > filter is good enough, I still might not get a sample right at the peak. > > Is there a better way? > ___ > 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
Re: [music-dsp] BW limited peak computation?
I suggest the cubic spline interpolator. It expresses the underlying function as piecewise trinomial so that the maxima/minima can be computed by solving binomial equations. It is also known to be close to the ideal sync interpolation alias-wise. Xue From: Paul Stoffregen___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
Re: [music-dsp] BW limited peak computation?
2016-07-25 23:00 GMT+02:00 Paul Stoffregen : > > Does anyone have any suggestions or references for an efficient algorithm to > find the peak of a bandwidth limited signal? > > If I just look only at the numerical values of the samples (yeah, that's what > I've been doing), when a signal is close to an integer division of Fs, even > collecting data over many cycles tends to miss the phases of the waveform > containing the peaks. For example: > > Image also available here: > https://forum.pjrc.com/threads/35478-Problems-Plotting-Filter-Response?p=110442&viewfull=1#post110442 > > The only solution I'm imagining would involve expensive upsampling and > filtering. Even then, if I multiply the sample rate by 16 or more and the > filter is good enough, I still might not get a sample right at the peak. > > Is there a better way? I'm no special expert in these matters, however I'll try to help. AFAIK it really depends on the application. As you noticed, just comparing sample values is not always sufficient, and that is the case when the signal has relatively strong frequency components not too far from the Nyquist limit (well, I mean, something like fs/10 or something like that). Then, you obviously do need some sort of resampling/interpolation (or at least, I don't know any cheaper alternative to that). IIRC, the ITU-R BS.1770 even goes as far as suggesting a specific 4x polyphase filter to cope with this problem somehow (I guess it was was the "true peak meter" thing... I guess you easily can check it yourself). Otherwise, you might very well use higher-order (i.e., not just linear) interpolators, (e.g., not-a-knot cubic spline interpolator), and check for first derivative sign change on the "reconstructed" part of the signal. This is most likely much cheaper, but also more "risky", as its precision could be very sensitive to the kind of input signal you have. In both cases, you need to careful about Gibbs (resampler) / Runge (interpolator) phenomena. Theoretically speaking, if your signal is "perfectly bandlimited", Gibbs fluctuations would indeed be "valid", but in the real world that's probably not the case. So... according to my limited knowledge, it all boils down to what you are really trying to do. Hope this helps somehow, -- Stefano D'Angelo http://sdangelo.github.io/ ___ dupswapdrop: music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
