Headroom & inter-sample overs

Omid

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I just thought I'd share another little trick to increase gain a bit more (only a relevant issue if you have a low gain system, or less efficient speakers). Skip this post if you can play plenty loud enough.

Roon adds the option to lower gain by a few dB for headroom. The idea is that your digital signal can never exceed 0dBFS, but the analog sine wave that connects the dots can peak higher. Benchmark audio explains it better than I can (article). Here's a picture that illustrates the idea:
1670211260857

Some DACs (like Benchmark) can play this analog sample without clipping (as long as the peak is <3.5 dB above 0dBFS), but most DACs will clip the top of the signal. So Roon's headroom management is quite useful. These inter-sample overs are actually not rare in music tracks (especially at 1/4 of the frequency of the sampling rate). From a couple of tests I did it seems they occur more in the higher frequencies.

When we create a filter in Audiolense, we often attenuate the signal especially in the higher frequencies (down sloping target curve). So it's possible that an Audiolense filter will decrease the need for headroom management. There is a way to measure this !

I've attached a white noise wave file with a 44100 Hz sample frequency that has numerous intersample overs (up to +8dB above 0dBFS), through all frequencies. Make sure you don't play it on your stereo you might damage your speakers. There is free software that can analyze tracks and count the number of inter-sample peaks (ISP). I use adobe audition. I upsample the sampling frequency (to 384,000Hz) and extract the info. Here's the file. Notice how the peak in this picture reaches +6dBFS:
1670212952982


And here is the amplitude statistics (8.12dB peak, 1,548,140 clipped samples in a 10 second track!):
1670213008674


Now I upload the track in JRiver, and convolve the 44,100 Hz test track with my DSP filter. Then I load the convolved track (6 tracks in my case due to crossovers etc) back in Adobe audition and upsample it again.
then do the same analysis and see what happens to the peaks (here's my worst channel):
1670213483851



We're down from +8.12 to +4dB peaks and clipped samples are down to 64,238. Keep in mind that this is a torture test track. If 3 or 3.5 dB headroom is ok for most music tracks, then my Audiolense filter is already sufficiently attenuating the signal. So in my case I don't necessarily need Roon's headroom management.

I hope that makes sense and helps someone.
 

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