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Aha!

Posted by Charles Hansen (M) on June 6, 2017 at 19:01:41

In Reply to: RE: OK, now we are on the same page - it is aliasing *and* it is a bug. posted by Jim Austin on June 6, 2017 at 14:34:09:

OK, now I get it!

I was wrong and you were right, and now I understand where I was led astray with regards to the aliasing. I only read JA's Brooklyn review close enough to notice the single-rate MQA filter response just recently (even though it is ~9 months old) and it hadn't fully sunk in. Instead I've been operating under the (presumably still accurate) premise that the limiting factor in the MQA "end-to-end system response" was the digital reconstruction filter (in the D/A converter), which at the quad-rate sampling frequency yields this frequency response curve:

and mistakenly assuming that was the filter also being used with single-rate audio data. I now completely agree with your analysis using your measured spectra combined with (the other) JA's measurements of the Brooklyn single-rate filter.

And now we also an see the likely reason why the notch appears in the spectrum of single-rate MQA files originally recorded at 44.1kHz. Virtually all digital equipment (recording or playback) uses "halfband" digital filters, as these require only half as many taps and half as much storage for the memory coefficients. One key characteristic of a halfband filter is that it will always have a response of -6dB at the Nyquist frequency (Fs/2).

If that output is later fed to a "leaky" reconstruction filter that mirror-images the audio data as out-of band aliases, there will be a continuous graph with no gap between the original music and the aliased version. But that is not what we see in your Beyonce track. Instead it appears that at some point the audio data was fed through an "apodizing" filter, specifically designed to filter out the "ringing" created by the anti-aliasing filter of the A/D converter at the Nyquist frequency (Fs/2). I would guess that this was part of the MQA process, as I am unaware of any commercially available A/D converters with built-in "apodizing" filters.

When that filtered audio data is then sent through yet another digital filter - this time the "leaky" MQA filter in the D/A converter, the sharp rolloff between 21kHz and 22kHz seen in your original spectrum of the Beyonce track is mirror-imaged at 22.05kHz due to the aliasing. The combination of the "apodizing" filter and the "leaky" MQA filter creates the "notch" seen in the spectrum. Thank you for your input in helping to solve this mystery!

As far as MQA's claim that 32dB of anti-aliasing is sufficient for signals in the 0 (DC) to 7kHz range, I think that is open for debate. It would seem that high-performance audio generally revolves around the idea of continuous improvement, and not dictating "sufficient" levels of performance.

As always, solely my own opinions and not necessarily those of my employer or butcher.

This post is made possible by the generous support of people like you and our sponsors:

Analog Engineering Associates

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