In a series of recent feature articles for Stereophile, Jim Austin has examined how the controversial MQA codec works: “MQA Tested, Part 1,” “MQA Tested Part 2: Into the Fold,” “MQA Contextualized,” “MQA, DRM, and Other Four-Letter Words,” and, most recently, “MQA: Aliasing, B-Splines, Centers of Gravity.” I doubt there is a Stereophile reader who is unaware of the fracas associated with MQA, and I have been repeatedly criticized on web forums for describing its underlying concept as “elegant.”
But elegant it is, I feel. MQA Ltd.’s Bob Stuart has described the goal of MQA as being to reduce to “plumbing” everything between the original analog signal fed to the analog/digital (A/D) converter and the analog signal output by the digital/analog (D/A) converter, other than routing the signal from the original event to the end-user’s system. In other words, the A/D conversion of the output of the microphone preamps (in a purist recording) or the mixing console (in a conventional recording), the transmission, storage, and subsequent D/A conversion will be transparent, except for an ultrasonic rolloff equivalent to a signal path of a few feet in air.
Of course, there will still be the limitations of the sample rate and bit depth chosen for the conversion of analog to digital, and in this article I examine what happens when that conversion takes place and the implications for MQA.
D/A Conversion
An A/D converter works by sampling and encoding the original analog signal and producing a datastream consisting of a regular string of numbers. Each number describes the amplitude of the signal at a time interval 1/S second after the previous one (S is the sampling frequency). To reconstruct the signal, this stream of data is fed to a D/A converter that outputs a pulse every 1/S second, the height of the pulses approximately mapping out the analog signal’s original shape. (Practical DACs use a sample-and-hold circuit to turn each pulse into a DC voltage step, but that is immaterial to the point.)
As outlined by Claude Shannon in his classic 1949 paper (footnote 1), for theoretically perfect waveform preservation, the bandwidth of the signal to be sampled needs to be restricted to half the A/D converter’s sample rate by what is called an antialiasing filter. However, the spectrum of the sampled data doesn’t extend to half the sample rate, as you might expect (fig.1); it extends to an infinitely high frequency, the spectrum of the band-limited audio signal mirrored to either side of the sample rate and every one of its harmonics (fig.2). When the digital data are used to re-create the analog signal, these ultrasonic “images” need to be eliminated. This is performed by the D/A converter’s reconstruction filter, so called because, as well as removing the ultrasonic images, it reconstructs the original band-limited analog signal not just at the sampling points in time but between those points.
Fig.1 Audioband spectrum of original musical signal.
Fig.2 Spectrum of same musical signal after being sampled and converted to digital.
In one of the first articles I wrote for Stereophile, in 1986, I examined how the impulse response of the D/A converter’s reconstruction filter is fundamental to this process. In engineerspeak, the digital filter convolves the digital audio data with the filter’s impulse response. A digital filter comprises a series array of multiplication units or “taps,” each separated in time by a single sample delay, and with a summing unit fed the outputs of every multiplier to create the filtered output data fed to the DAC. As the first data word is fed to the first multiplier, it’s multiplied by the coefficient stored for that multiplier, and is then fed to the second multiplier as the next data word is fed to the first multiplier—and so on until the data exit the final multiplier, the sum of the multiplier outputs at each sampling instant exactly reproducing the bandwidth-limited, but now filtered waveform.
If you plot this series of filter coefficients against time, you get the familiar filter impulse response that I publish in our reviews of digital processors (fig.3). The kind of filter shown in this graph, which offers a very steep rolloff above the passband, is almost ubiquitous in digital audio products. The actual shape of this filter’s time-domain response is called a (sin x)/x or sinc function curve. The “ringing” occurs at exactly half the sample frequency, called the Nyquist frequency, extends in time (in theory) from minus infinity to plus infinity, and decays very slowly on either side of the central peak. This filter is linear-phase in nature, meaning that there is no phase distortion; however, the more you constrain the data in the frequency domain, the less you can do so in the time domain, and a sinc-function filter smears the transient’s energy in an extreme manner.
Fig.3 Conventional D/A converter, linear-phase impulse response (one sample at 0dBFS, 44.1kHz sampling, 4ms time window).
In natural sound, echoes always occur after a sound—never before. This pre-echo is therefore unnatural; and while a continuous waveform will be reconstructed correctly, it is possible that the pre-echo might well be heard as a degradation with a discontinuous waveform, such as musical transients (see later).
A/D Conversion
But what about the other end of the process, where the analog signal is converted to a digital datastream? All modern A/D converters are sigma-delta types in which a converter with a limited bit depth operates at an extremely high sample rate. A digital decimation filter is then used to create the conventional multi-bit PCM datastream sampled at the familiar rates: 44.1kHz and its multiples, 48kHz and its multiples. This filter will overlay its own impulse response on that datastream, and this is when time smear—what Bob Stuart calls temporal blur—raises its head.
To examine the response to an impulse of a D/A converter’s reconstruction filters, I use a test signal I created that comprises 16-bit/44.1kHz “digital black” or silence into which I inserted a single sample at full scale to create the shortest possible pulse at this sample rate. While this isn’t a signal a DAC will encounter with music data, a DAC’s response to this single sample “maps” the coefficients of its reconstruction filter. To characterize the antialiasing filter of an A/D converter, therefore, I first thought about using a signal generator to create a similarly short analog pulse—back in the late 1980s, I built a monostable multivibrator circuit with adjustable pulse width for this purpose. But while that analog pulse would indeed reveal the antialiasing filter’s impulse response, A/D converters would never be confronted with such a signal in real life. For the tests I’m about to describe, therefore, I felt it more appropriate to use an analog test signal that approximated music.
Using the pencil tool supplied with the BIAS Peak program (no longer available), I drew several arbitrary impulse-response waveforms sampled at 384kHz. These ranged from a simple square pulse to various shaped pulses of various lengths, as well as an asymmetrical triangular impulse similar to the MQA test-signal waveform shown on p.139 of our January 2018 issue. My goal was to present the ADC with a signal that gently rolled off above the audioband and had no significant energy above 60kHz. (Work by Bob Stuart and others has shown that 60kHz is the approximate upper limit of music information.) Fig.4 shows the waveform of the impulse I created—it peaks at –3dB, so there’s no danger of converter overload—and fig.5 shows its spectrum. The vertical green line to the right of this graph is placed at 60kHz—you can see that the signal’s content above 60kHz is down at least 20dB from the audioband level. The spectrum is white rather than pink, but this doesn’t affect the measurements.
Fig.4 Digital-domain impulse-response test waveform sampled at 384kHz.
Fig.5 Spectrum of impulse-response test waveform (10dB/vertical div.).
To create the analog equivalent of this digital signal, I used the Pure Music 3.0 app on my MacBook Pro to send the impulse data to a Mytek HiFi Brooklyn DAC via USB. As the signal’s sample rate was 384kHz and I was going to test the A/D converters at sample rates of 48 and 96kHz, the ringing of the Brooklyn’s own reconstruction filter at 192kHz would be one or two octaves above the respective Nyquist frequencies and would not affect the results.
I needed to examine the A/D converters’ reaction to this analog pulse in the digital domain. I therefore used the Metric Halo MIO2882 FireWire interface I use both to make music recordings and to test speakers. The MIO2882 has both analog and digital inputs, and I recorded its digital output data on a Mac mini.
As well as the Metric Halo, I had two other ADCs to hand: the Ayre Acoustics QA-9 I’d bought after reviewing it in November 2012 (footnote 2) and the newer of the two dCS 904s I purchased nearly 20 years ago to make high-resolution recordings. I recorded the digital outputs of the Ayre and dCS converters by feeding them to the MIO2882’s AES/EBU digital input and to test the MIO2882, I fed the Mytek Brooklyn’s analog outputs to the MIO2882’s analog inputs.
I’ve shown only the behavior of the ADCs operating at 96kHz. (The 48kHz behavior was identical, allowing for the effect of the lower sample rate.) Looking first at the MIO2882, which uses an AKM converter chip, the resulting impulse response examined in the digital domain (fig.6) reveals that the antialiasing filter is a linear-phase sinc-function type, with both pre-ringing and post-ringing at 48kHz visible. In fig.7, I’ve expanded the vertical scale to ±6% to show the fine detail. Fig.8, which also has an expanded vertical scale, shows the impulse response of the dCS 904 with its sharp-rolloff F1 filter selected. This ADC, too, has a linear-phase antialiasing filter with significant pre- and post-ringing. Switching to the dCS’s slow-rolloff F4 filter (fig.9) dramatically reduces the amount of ringing, though this is still a linear-phase filter, with one cycle of pre- and post-ringing.
Fig.6 Metric Halo MIO2882, digital-domain impulse response (96kHz sample rate).
Fig.7 Metric Halo MIO2882, digital-domain impulse response (96kHz sample rate), with expanded vertical scale.
Fig.8 dCS 904, F1 filter, digital-domain impulse response (96kHz sample rate), with expanded vertical scale.
Fig.9 dCS 904, F4 filter, digital-domain impulse response (96kHz sample rate), with expanded vertical scale.
By contrast, the Ayre QA-9’s Measure filter (fig.10) is a minimum-phase type, with no pre-ringing (footnote 3). It’s also “short,” with very little post-ringing visible. But the surprise of the bunch is the Ayre with its Listen filter selected (fig.11)—no pre- or post-ringing is visible, and other than the fourfold reduction in sample rate, the shape of the original impulse has been preserved.
Fig.10 Ayre Acoustics QA-9, Measure filter, digital-domain impulse response (96kHz sample rate).
Fig.11 Ayre Acoustics QA-9, Listen filter, digital-domain impulse response (96kHz sample rate).
Footnote 1: Proceedings of the IRE, January 1949, Vol.37 No.1, pp.10–21. Reprinted in Proceedings of the IEEE, February 1998, Vol.86 No.2, pp.447–45. See https://web.archive.org/web/20100208112344/http://www.stanford.edu/class/ee104/shannonpaper.pdf.
Footnote 2: The QA-9 has since been discontinued, but Ayre had a limited production run in early 2018.
Footnote3: Although Charley Hansen and Bob Stuart disagreed on almost everything audio-related, they shared an antipathy for linear-phase filters.
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