I shouldn't have been surprised. When I interviewed Charley Hansen (who, sadly, passed away in November 2017) in 2012 about the design of the QA-9, he explained that "instead of using the normal low-pass Finite Impulse Response (FIR) filter to turn the output of the delta-sigma DAC into PCM, we use a moving-average filter. This doesn't just allow for improved transient response, but actually perfect transient response. . . . There is no pre-ringing, no post-ringing—no ringing whatsoever."
Sample-Rate Conversion
These results reveal that, with the exception of the dCS 904 with its F4 slow-rolloff filter and the Ayre QA-9 in Listen mode, the signal, after being brickwall-filtered during A/D conversion, has been significantly altered from the original. Transients are smeared out in time both before and after the event by the converter's ringing at its Nyquist frequency. With CDs made from original analog signals that have been sampled at 44.1kHz, this ringing will be at 22.05kHz and, as you can see later, will not be removed by the DAC's reconstruction filter. However, it is increasingly common for digital master recordings to be made at sampling rates higher than 44.1kHz. The CD master is prepared by using a sample-rate converter, and the A/D converter's ringing at its Nyquist frequency will be an octave or more above the CD's passband. So if the master is sampled at 96kHz, for example, won't the ADC's time smearing be eliminated? To answer this question, I took the 96kHz pulse captured by the Ayre QA-9 in Listen mode and used the highest-quality sample-rate converter in BIAS Peak to downsample it to 44.1kHz. The result is shown in fig.12. Despite the original digital data having perfect time-domain behavior, the sample-rate converter's low-pass digital filter has introduced our old friend linear-phase, sinc-function, acausal ringing, this time at the new Nyquist frequency of 22.05kHz. Again, this temporal blur now becomes part of the signal reconstructed by the DAC (footnote 4).
With rare exceptions, the ringing at the sample rate's Nyquist frequency is ubiquitous with A/D converters. However, it's difficult to see why this should matter. While there will be some few listeners who hear a tone at 22.05kHz with CD data, no one will hear a 48kHz tone with data sampled at 96kHz, or a 96kHz tone with 192kHz data.
Keith Howard investigated the "energy smear" exhibited by digital filters in January 2006, writing that "the time-domain performance of anti-alias and reconstruction filters has increasingly been blamed for CD's residual failings." However, he concluded that the listening tests described in that article showed that the energy smear "seemed surprisingly reluctant to show its face"; only in one extreme case—a filter in which all the ringing occurred before the impulse—did this energy smear prove consistently audible in listening tests.
Nevertheless, I understand that the ear/brain acts as a detector of wavefront arrivals, and that the pre-ringing of an acausal digital filter causes confusion: the initial onset of the ringing and the arrival of the maximum energy peak are incorrectly interpreted as two separate events rather than as one—as implied by Bob Stuart in his June 2018 interview with Jim Austin.
This might be one reason listeners prefer the sound of recordings made with higher sample rates (footnote 6). With 96kHz data, the time delay between the beginning of the sinc-function envelope and the maximum energy peak will be less than half what it is with CD data, and with 192kHz data it will be less than one-fourth that duration. Each time the sample rate is doubled, the time delay—and thus the confusion—will be half what it was before.
But what can be done to eliminate this confusion?
To a large extent, designing a D/A converter with a reconstruction filter that preserves time-domain accuracy and is free from pre-echoes is a "solved" problem. Almost since the launch of the Compact Disc, DAC designers have developed reconstruction filters that better preserve transient information. Two early examples were Wadia's DigiMaster filter and Pioneer's Legato Linear filter, both from the end of the 1980s—and many modern D/A processors offer a choice between such slow-rolloff, "gentle" reconstruction filters and ones that constrain the signal more in the frequency domain, at the expense of the time domain. MQA's reconstruction filter, for example, is a slow-rolloff type intended to preserve the timing of transients.
The trade-off these "gentle" filters offer for the preservation of the time-domain performance is a slight rolloff in the top audio octave and the increased possibility of image energy leaking into the audioband. As Charley Hansen wrote in a posting to the Audio Asylum web forum in 2004, "A gentle filter . . . becomes a trade-off between high-frequency rolloff and out-of-band energy. Most manufacturers choose a compromise with some high frequency rolloff and some out-of-band energy. . . . Most music has very little energy close to the Nyquist frequency. . . . [A]ny theoretical problems with out-of-band energy are probably no worse than the out-of-band energy found on LPs when played back with MC cartridges."
But what if the D/A processor has no reconstruction filter at all? By definition with these non-oversampling (NOS) DACs, there will not be any new Nyquist-frequency ringing, which might be why some listeners prefer them to DACs with digital filters. However, the ultrasonic images of the audioband spectrum are there in full force with such DACs and this will be less of a problem with high-sample-rate data than with CD data, a point made by Hansen in his 2004 posting. But the presence of this high level of ultrasonic energy may well lead to slew-rate limiting, hence distortion, with preamplifiers and amplifiers. And NOS DACs faithfully reproduce the A/D converter's Nyquist ringing on the recording.
Before he passed away at the end of November 2017, Charley Hansen and I were having a long e-mail exchange about digital filters. He sent me some measurements showing the behavior of experimental complementary slow-rolloff filters that he and his team had developed for both A/D and D/A conversion. The goal was to optimize the digital chain's behavior in the time domain by using a very "short" antialiasing filter at the A/D conversion (like the Ayre QA-9's Listen filter), and a similarly "short" reconstruction filter when the digital data are decoded. "The double- and quad-rate filters," he wrote, "are essentially the converse of the double- and quad-rate filters on the QA-9." The measurements were convincing. An analog signal encoded with Ayre's Listen filter, then decoded with the experimental complementary filter, was reproduced with perfect time-domain performance. The tradeoffs in the frequency domain were a rolloff in the top audio octave that reached –4dB at 20kHz with a 96kHz sample rate, equivalent to 6m of air.
Charley Hansen was a vociferous critic of MQA. However, if you compare what I've written in the paragraph above with my earlier description of the goal of MQA's developers, they are, in essence, identical! The impulse encoded at 96kHz with the Ayre QA-9's Listen filter and decoded with the Mytek Brooklyn's upsampling MQA filter is reproduced with its time-domain behavior preserved (fig.16)—in other words, from analog original to analog re-creation, there is no temporal blur.
The QA-9's Listen filter is a special case. But if MQA's removal of "temporal blur" is equivalent to MQA having eliminated the Nyquist-frequency ringing introduced by the antialiasing and decimation filters of conventional A/D converters, then the end result will be as if all of the recordings encoded with MQA were made with the Ayre QA-9—a fitting if unexpected tribute to Charley Hansen.
Footnote 4: The exception is the upsampling "apodizing" reconstruction filter developed by Peter Craven and used in Meridian DACs, which has a null at the CD's Nyquist frequency. Footnote 5: Although it is possible to set the Mytek Brooklyn to use its upsampling MQA filter with regular PCM data, that is not the same as one of the set of MQA reconstruction filters, which is controlled by the encoder. These MQA filters are complementary to the set of anti-aliasing filters used by the MQA encoder.
Footnote 6: Joshua D. Reiss, A Meta-Analysis of High Resolution Audio Perceptual Evaluation." JAES, June 2016, Vol.64 No.6, pp.364–379.
These results reveal that, with the exception of the dCS 904 with its F4 slow-rolloff filter and the Ayre QA-9 in Listen mode, the signal, after being brickwall-filtered during A/D conversion, has been significantly altered from the original. Transients are smeared out in time both before and after the event by the converter's ringing at its Nyquist frequency. With CDs made from original analog signals that have been sampled at 44.1kHz, this ringing will be at 22.05kHz and, as you can see later, will not be removed by the DAC's reconstruction filter. However, it is increasingly common for digital master recordings to be made at sampling rates higher than 44.1kHz. The CD master is prepared by using a sample-rate converter, and the A/D converter's ringing at its Nyquist frequency will be an octave or more above the CD's passband. So if the master is sampled at 96kHz, for example, won't the ADC's time smearing be eliminated? To answer this question, I took the 96kHz pulse captured by the Ayre QA-9 in Listen mode and used the highest-quality sample-rate converter in BIAS Peak to downsample it to 44.1kHz. The result is shown in fig.12. Despite the original digital data having perfect time-domain behavior, the sample-rate converter's low-pass digital filter has introduced our old friend linear-phase, sinc-function, acausal ringing, this time at the new Nyquist frequency of 22.05kHz. Again, this temporal blur now becomes part of the signal reconstructed by the DAC (footnote 4).
Fig.12 Digital-domain impulse response captured by Ayre Acoustics QA-9, Listen filter, at 96kHz, downsampled to 44.1kHz.
This can be seen in fig.13, which shows the analog output of the Mytek Brooklyn, set to use its short MQA reconstruction filter, when fed the Ayre QA-9's 96kHz-sampled pulse downsampled to 44.1kHz. (I used the MQA filter, as its own impulse response has minimal ringing and won't confuse the result, footnote 5.) The rate conversion filter's pre- and post- ringing at 22.05kHz has been affected by the MQA filter's minimum-phase impulse response (fig.14) but has not been eliminated. However, it is fair to note that the MQA filter's slow rolloff will not significantly attenuate content at 22.05kHz. I therefore repeated the test using the Brooklyn's FR (Fast Rolloff) filter. This will attenuate the data's ringing at 22.05kHz, but as you can see from fig.15, it appears to have substituted its own acausal ringing. (Note that the digital data has already been band-limited to half the 44.1kHz sample rate, thus is a "legal" signal.) The implication of this result is that with a musical transient, ie, when there is silence then data, the continuous waveform is exactly reconstructed after the transient, but before the transient there will be the sinc-function pre-echo present in the reconstructed signal.
Fig.13 Impulse response at 44.1kHz from fig.12, converted to analog with Mytek HiFi Brooklyn using the latter's MQA upsampling filter.
Fig.14 Mytek HiFi Brooklyn, MQA upsampling filter, impulse response at 441.kHz.
Fig.15 Impulse response at 44.1kHz from fig.12, converted to analog with Mytek HiFi Brooklyn using the latter's FR reconstruction filter.
And many listeners report that there is an improvement with transient sounds. I have written, for example, that a very quiet tick in the original WAV file of a choral recording, the Portland State Chamber Choir performing Eric Whitacre's Water Night, sounded more like a sound made by a human being in a real space in the MQA version.
What This MeansWith rare exceptions, the ringing at the sample rate's Nyquist frequency is ubiquitous with A/D converters. However, it's difficult to see why this should matter. While there will be some few listeners who hear a tone at 22.05kHz with CD data, no one will hear a 48kHz tone with data sampled at 96kHz, or a 96kHz tone with 192kHz data.
Fig.16 Impulse response captured by Ayre Acoustics QA-9, Listen filter, at 96kHz, converted to analog with Mytek HiFi Brooklyn using the latter's MQA reconstruction filter.
Footnote 4: The exception is the upsampling "apodizing" reconstruction filter developed by Peter Craven and used in Meridian DACs, which has a null at the CD's Nyquist frequency. Footnote 5: Although it is possible to set the Mytek Brooklyn to use its upsampling MQA filter with regular PCM data, that is not the same as one of the set of MQA reconstruction filters, which is controlled by the encoder. These MQA filters are complementary to the set of anti-aliasing filters used by the MQA encoder.
