Avoiding inter sample peaks

To play sound our ears and brain understand, a digital audio system must emit an analog signal. The switch from digital to analog is handled by the digital-to-analog converter, usually just called a DAC.

Under specific conditions, which I describe below, the DAC can produce an analog signal that momentarily exceeds the level of the digital signal from which it was converted. This is known as an inter-sample peak, and while it may at first seem just a curious side effect of the conversion process, these peaks have implications for anyone working with digital audio. And in particular, engineers who like "hot" mixes.

Digital Audio - grossly over-simplified

Computers process numbers, so to work with audio in a computer, we must convert the sound into numbers. This is accomplished by "sampling" the audio signal at regular intervals - 44,100 times a second for CD audio - and saving the observed level. The diagram below illustrates this, albeit crudely. The samples in red, numbered 1 to 9, represent a sequence of signal levels observed by the recording interface.

You can see something similar by zooming-in on a waveform in any recording software. The "step-ladder" model illustrates the discrete samples of digital audio, with levels ranging from "-inf" (silence) to 0 dBFS (the loudest sound a digital system can represent [*]) However, sound outside a computer doesn't move through the air in jagged, abrupt steps. Rather, it moves smoothly and continuously - more like the blue line in this diagram.

Digital to analog conversion, then, is essentially the creation of the smooth blue analog line from the set of stepped red digital samples.

Intersample peaks

Occasionally, the smoothing yields an interesting result, illustrated below. Note that in order to generate a smooth curve between samples 5 and 6, the DAC produces a signal that peaks higher than either of the samples. This is an inter-sample peak.

This diagram also illustrates the main issue with these peaks: Samples 5 and 6 are both at 0 dBFS - that is, they represent the loudest sound the digital system can reproduce. Yet the peak analog signal reconstructed by the DAC exceeds this level.

In short, the DAC in this example has generated an invalid signal.

How does it sound?

What this means in practice depends on a few factors, including the quality of the DAC, and the signal chain after the converter.

In the worst case, the example above would result in audible clipping when the system tries to generate the illegal voltage. But even if no clipping occurs, the analog side of the DAC will only handle the signal cleanly if the DAC's analog circuitry has some headroom. If the DAC's designers assumed that 0dBFS is the loudest signal the converter will emit (technically, a valid assumption,) then an analog peak above this level will cause distortion.

Here's a short clip I deliberately mixed hot. There's no digital clipping (the maximum sample level is -0.1dBFS,) but there are lots of inter-sample "errors", including a nasty string of them at 0:13.

If you hear any pops or clicks, it's a good sign that your setup doesn't allow for inter-sample clipping. Most likely, though, the track sounds just fine to you. Many systems, especially those equipped for mixing audio, allow some head room between the maximum digital signal level and the onset of analog distortion.

But not every system… If you mix hot, especially if your meters peak within 1dB of full scale, your mixes probably contain these peaks. And though your DAC protects you, there's no guarantee that your listeners have quality converters. In other words, you may be sharing clipped or distorted audio without realizing it!

Preventing inter-sample clipping

There are at least 3 ways to ensure your mixes don't generate inter-sample distortion:

1. Leave lots of headroom in your mix: This is the obvious solution, and it requires no special processing. As long as you keep the peak levels in your mix below 0dBFS, the DAC will never encounter the situation described above. The consensus I've found is that real-world inter sample peaks never exceed 1dB, so keep your levels below -1.0 dBFS and you'll be fine.

2. Use a mastering tool designed to prevent these peaks: iZotope's Ozone is one such tool. The loudness maximizer has a one-click option to prevent inter-sample clipping.

3. Use a metering tool that highlights the peaks: SSL recently released the X-ISM Plug-In which adds an inter-sample peak meter to any VST-capable DAW.

X-ISM uses significant processing to provide a combination of up-sampling and filtering that mimics the operation of an oversampling DAC’s reconstruction process. The result is a meter that shows inter-sample errors and provides a useful tool that most DAW metering misses.

More reading

Along with the page on SSL's site, above, here are a few more links that explore the issue in detail:

- 0 dBFS explained

- Chris Tham's Issues with 0dBFS+ Levels On Digital Audio Playback Systems

- This classic thread on ProSoundWeb (especially the posts by Paul Frindle) presents head-spinning amounts of information. I recommend re-reading it every few months.

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Tags: mixing