Hi folks, the audio world is sort of obsessed with sort of "true peak level". Unfortunately it is rather tricky to calculate, so it is calculated by oversampling to about 192kHz and taking the normal peak level. Sadly that's really not true peak level. So how about the (nearly) correct value - if we take say 2 * N + 1 samples around each sample S[0] (hence S[-N] .. S[N]), we can calculate any value between S[0] and S[1] using sinc interpolation. All we need to do is to calculate the maximum between these 2 samples. Has anyone attempted to do it analytically (hence hopefully efficiently)? I started messing with it and the derivatives (for the classic f' == 0) are just way too ugly. Numeric approach could work, but the accuracy would be lower again and it could take way too much CPU power. --------------------------------------- Posted through http://www.DSPRelated.com

# Finding maximum of sinc in 0..1

Started by ●September 5, 2017

Posted by ●September 6, 2017

On Tuesday, September 5, 2017 at 12:12:44 PM UTC-7, jungledmnc wrote:> Hi folks, > > the audio world is sort of obsessed with sort of "true peak level". > Unfortunately it is rather tricky to calculate, so it is calculated by > oversampling to about 192kHz and taking the normal peak level. Sadly > that's really not true peak level. > > So how about the (nearly) correct value - if we take say 2 * N + 1 samples > around each sample S[0] (hence S[-N] .. S[N]), we can calculate any value > between S[0] and S[1] using sinc interpolation. All we need to do is to > calculate the maximum between these 2 samples. > > Has anyone attempted to do it analytically (hence hopefully efficiently)? > I started messing with it and the derivatives (for the classic f' == 0) > are just way too ugly. Numeric approach could work, but the accuracy would > be lower again and it could take way too much CPU power. > --------------------------------------- > Posted through http://www.DSPRelated.comIt should be close enough to a parabola over a small region around the peak.

Posted by ●September 6, 2017

On 2017-09-06, herrmannsfeldt@gmail.com <herrmannsfeldt@gmail.com> wrote:> On Tuesday, September 5, 2017 at 12:12:44 PM UTC-7, jungledmnc wrote: >> Hi folks, >> >> the audio world is sort of obsessed with sort of "true peak level". >> Unfortunately it is rather tricky to calculate, so it is calculated by >> oversampling to about 192kHz and taking the normal peak level. Sadly >> that's really not true peak level. >> >> So how about the (nearly) correct value - if we take say 2 * N + 1 samples >> around each sample S[0] (hence S[-N] .. S[N]), we can calculate any value >> between S[0] and S[1] using sinc interpolation. All we need to do is to >> calculate the maximum between these 2 samples. >> >> Has anyone attempted to do it analytically (hence hopefully efficiently)? >> I started messing with it and the derivatives (for the classic f' == 0) >> are just way too ugly. Numeric approach could work, but the accuracy would >> be lower again and it could take way too much CPU power. >> --------------------------------------- >> Posted through http://www.DSPRelated.com > > It should be close enough to a parabola over a small region around the peak.Nowhere near good enough. These are golden-eared audiophiles we're talking about, the ones who can hear the difference between using any old power cord for their amplifier and the ones costing $10k plus. I'm not joking (about the price).

Posted by ●September 6, 2017

On Tuesday, September 5, 2017 at 8:20:59 PM UTC-5, Fred Smith wrote:> Nowhere near good enough. These are golden-eared audiophiles we're > talking about, the ones who can hear the difference between using > any old power cord for their amplifier and the ones costing $10k > plus. I'm not joking (about the price).First of all, what is the *true* value? You can say that the peak value of the source analog waveform is the true value, but as soon as you introduce an antialiasing filter (nowadays antialiasing filters generally have few, if any, analog components) that is no longer true. Sinc interpolation will give the optimum band-limited estimate, assuming that the passband is rectangular. But it's never actually rectangular. Oversampling and interpolating make their own similar assumptions. How can you know which one is closest to the *true* value when you don't know what the true value is? Which brings me to the second point: all signals are noisy. You can only determine the actual peak value to within a tolerance dictated by the noise in its vicinity. I have implemented 2nd-order and 4th-order parabolic estimators to find peak intersample values, and they are quite close to the full-on sinc estimation. Close enough? That's a judgment call. https://dspguru.com/dsp/howtos/how-to-interpolate-fft-peak/

Posted by ●September 6, 2017

Well, I assume the oversampling filters used by any device afterwards (D/A, lossy compression, which would cause some additional problems though...) will be linear-phase (otherwise one can make no assumptions after all). If that would be true, resampling to any sampling rate would pick up various points of the "virtual analog" waveform defined by the actual samples S[i]. If we can find the actual maximum of this virtual analog waveform, then no oversample can ever peak over 0dBFS. The point of this true peak thingy is that the D/A is oversampling internally, so in theory even if your waveform doesn't get over 0dBFS, the oversampled waveform could. But since it is measured by oversampling to 192kHz, it only improves the estimate, but it doesn't really say the correct value. Additionally if we could measure the value accurately, we could use it for actual true-peak limiting (as opposed to what true-peak limiting means now - just oversampled limiting...). --------------------------------------- Posted through http://www.DSPRelated.com

Posted by ●September 6, 2017

I forgot - parabolic estimation may get you something, but these are not fft bins, I don't think it would work close enough at all. One would need to use like 30 samples (my guess from sinc coefficient tables I'm using for actual interpolation). --------------------------------------- Posted through http://www.DSPRelated.com

Posted by ●September 6, 2017

On Wednesday, September 6, 2017 at 7:21:29 AM UTC-5, jungledmnc wrote:> Well, I assume the oversampling filters used by any device afterwards > (D/A, lossy compression, which would cause some additional problems > though...) will be linear-phase (otherwise one can make no assumptions > after all).Linear phase is not enough to guarantee that the interpolated peak will resemble the actual peak. Filter impulse responses overshoot and ring.

Posted by ●September 6, 2017

On Wednesday, September 6, 2017 at 7:24:37 AM UTC-5, jungledmnc wrote:> I forgot - parabolic estimation may get you something, but these are not > fft bins,No, but the principle is the same. Duality applies.

Posted by ●September 6, 2017

>On Wednesday, September 6, 2017 at 7:24:37 AM UTC-5, jungledmnc wrote: > >> I forgot - parabolic estimation may get you something, but these arenot>> fft bins, > >No, but the principle is the same. Duality applies.Could you be more specific about the "duality"? I may be missing some part of information here. As for linear-phase - if we assume there won't be any filtering (the oversampling itself isn't filtering as it doesn't change the spectrum content), then if we find the actual true peaks, then this should be the real maximum for any oversampling rate imho and no overshoots can happen. --------------------------------------- Posted through http://www.DSPRelated.com

Posted by ●September 6, 2017

On Wednesday, September 6, 2017 at 12:12:25 PM UTC-5, jungledmnc wrote:> Could you be more specific about the "duality"? I may be missing some part > of information here.You can interpolate between FFT bins or you can interpolate between samples. The mathematics are the same, only the domain changes.> As for linear-phase - if we assume there won't be any filtering (the > oversampling itself isn't filtering as it doesn't change the spectrum > content), then if we find the actual true peaks, then this should be the > real maximum for any oversampling rate imho and no overshoots can happen.If you don't filter then your inserted samples are all zero-valued. That interpolation will be the same as if you didn't upsample at all.