inter-sample peaks

[tomasrangel]

What is inter-sample peaks ? How bad is it ? How to fix it ?

I was reading about this at SSL page

Solid State Logic | Music

but i can´t understand it practically.

Can somebody help ?

Thx

[peeder]

It's not that bad. Relax.

Basically, because of the way the interpolator at the DAC works, you can have "over" voltages even in digital files that don't display any overs. Normal meters in DAWs don't display the voltages the DAC will generate, they only show the sample codes, and especially at low sample rates, you have plenty of room between them for the interpolator to generate a voltage above either of the sample codes. Usually these aren't louder than 1 decibel over the surrounding sample codes but in theory they can climb over 6db.

The only problem is that your DAC will generally not play them in a very linear fashion, and most (esp. cheaper) DACs are engineered to clip above full scale, which maximises their dynamic range spec. So those transients that exhibit intersample peaks will sound squared off (with lots of distortion) compared to peaks that stay under, say, -0.3dbFS. They might not sound so good, or on the other hand, you might enjoy the sound. However, every DAC will sound a bit different playing them back, because the DACs will clip at different levels. A high-end DAC might not clip at all, while a cheap consumer DAC might be very non-linear at anything above -6dbFS anyway.

Intersample peaks are used by the people fighting the loudness war as a means of stunning their opponents into hushed awe. But really, it's just another aspect of sound. Some people...including famous mastering engineers...just like the sound of clipping and do it intentionally. They would shrug off intersample peaks as just part of the overall sound. This fact really infuriates the anti-loudness contingent. They want linear transients and preservation of dynamics. And they know that if their masters are half a db softer than their competitors they will be thought of as worse sounding, because louder sounds better.

So you've stumbled upon a political conflict and all you need to know is that your meters aren't telling the whole truth about your level. An oversampling meter (e.g. TL MasterMeter) will show you your intersample peaks. Play-testing your masters on a variety of DACs will tell you more of what is really relevant, however.

[Nordenstam]

Perhaps the easiest way to think about it is that sample point meters are too slow. A VU meter is way slower than an analogue peak level meter. Similarly, sample point meters are way slower than reconstructed meters. There's plenty of time for the waveform to wiggle above or below the levels indicated by the relatively infrequent sample points.


Here's the standard reference: http://www.cadenzarecording.com/pape...distortion.pdf
More reading in TC library: Tech library


Have some pics on my webpage made for discussions on this topic. Although it's not as eloquent as the links above, it may be a supplement.

Part of the intersample peak problem is that the sample dots usually don't happen to land on the very top of the waveform - it's statistically way more probably to land on some other point than the very peak.



These two pics show (near) identical sine waves with a frequency very close to 1/4'th the sample rate(around 11025Hz). At some stages the sample points will hit at the peak of the waveform. At other, points, they will hit 1/4 further into the phase of the wave, almost 3dB lower. Upper pic is the wave shown in sound forge, which have a "non-reconstructed" waveform display. It's a connect-the-dots approach, that doesn't correlate with what happens at the output of the reconstruction in the converter(DAC). The sample point level meter in sound forge will track the sample dots and show a level that oscillates by almost 3dB, even though the output waveform is rock steady. The lower picture is the same wave shown in izotope RX, a program that does a reconstruction prior to visualizing the wave, showing it more like it'll appear on the DAC output. It's obvious here that the reconstructed output level should be steady, even though the sample points are all over the place.





The other part of the problem with getting the overview inside the computer is that reconstructed waveform have a final value that is not determined on a connect-the-dot basis, rather it's the sum of all the samples that brings the big picture together. Each sample point is not only effecting the level at that instant, it influences the final waveform hundreds of samples afar on each side of the sample point. This can create some really wild intersample peaks.

The picture below shows what a single sample looks like:



The upper row is the single sample shown with a connect-the-dots approach, the lower is the same single sample points after it have been low pass filtered. Everything that is reconstructed on the output of the DAC is filtered in a similar manner. Notice that the sample point values are always true. The peak of that impulse will always be the final waveform level at that instant. What is not known, from looking at the sample points, is what level the intersample land will be.

Looking at the same impulse in a calculator (sin(x)/x) makes it clearer how it's possible to have a bunch of sample points that does not grow when added up, while the land inbetween can grow almost arbitarily large if fed the right signal.



The wiggles on both sides of the impulse all goes to zero at regular intervals(the sample clock), except for the central point where the value is one. The contribution to the other samplepoints is zero at all times and one in the middle, but only for the sample points. The rest of the waveform, the intersample area, is reconstructed by summing a very large number of such impules.

(more in Dan Lavrys sampling paper: http://lavryengineering.com/document...ing_Theory.pdf )


And this is how the individual impulses works together:



The picture above shows what happens when a bunch of such impulses are summed. The upper line shows two lone samples, one positive and one negative. These are the bulding blocks of sampling. The lower row is total silence followed by a short burst of maximum frequency. Notice that the first two sample points are the same as the upper row, a maximum and a minimum value sample. The highlighted red parts, and a bunch more like them from the other samples, all adds up to create the intersample peak in the row below. (there are more intersample peaks there at other points too). Notice that this also show how audio sampling is able to preserve phase information, as the peak is displaced to the left with respect to the sample point.

The same things happens when anything changes fast on the waveform. Intersample peaks are often a product of imposing arbitary fast changes on the signal. Hard limiting and/or clipping are typical ways to do that. That is also a typical way to create aliasing (as fast changes equals high frequency and frequencies above 22050Hz have nowhere to go but manifesting themselves as alias). I personally think it's good engineering practice to avoid aliasing and intersample peaks, especially considering translation to lesser DACs and further processing like MP3 coding. But each to their own..

If you want to see something really bad on the oversampled meter - try a sequence of maximum and minimum values that goes like this: "1010101101010" - notice that the alternating 1's and 0's suddenly change direction in the middle. The results depends on the filter being used in the reconstruction, with the intersample peak easily exceeding 10dB!


Noisy square looking signals are often ripe with intersample peaks. I tried feeding a digital signal to the chain to look what peak levels occured. The result was this:


The left area is RMS and sample point metering, while the right meter shows reconstructed values. Notice that RMS shows up as -3dB, sample peak meter shows -4.5dB and the reconstructed meter shows the real peak to almost reach 1dB above zero. Musical signals are never this bad, although it sometimes leans towards results like these with the most abused victims in the loudness wars.

Hope this helps. =)


Regards,

Andreas Nordenstam

[tomasrangel]

Thats great.. i hope izotope loudness max tool can really prevent inter-sample peaks.

Thanks for help

[Alexey Lukin]

The exact amount of inter-sample overshoot depends on interpolation filters in D/A converter (this can also be examined by changing waveform interpolation order in RX). So, no limiter can completely remove inter-sample overshoots for all possible D/A converters. Ozone does the job to a reasonable extent.

[Nordenstam]

Originally Posted by tomasrangel

Thats great.. i hope izotope loudness max tool can really prevent inter-sample peaks.

Avoiding IS peaks and leaving half a dB of headroom is quite safe. Severe lossy coding will still make for clipped peaks, but it'll be safe in most other circumstances.

A recent thread on this: src conversion from 96Khz to 44.1 - gives volume / peak change

The most important thing for me is to watch the IS peak meter while doing processing. Some ways to tweak audio creates a lot of IS peaks and I prefer to avoid these at the source, rather than to slap a limiter on the end to band aid the problem.


PS: Alexey, thanks for the excellent software! Waiting in anticipation for RX to be VST compatible..


Andreas Nordenstam