Arcam FMJ D33 D/A processor Follow-Up, April 2013

Follow-Up, April 2013, the “Reis Test” (Vol.36 No.4):

In 1972, the late biologist Stephen Jay Gould made a convincing case for what he called "punctuated equilibrium": long periods of evolutionary stasis interrupted by brief periods of rapid evolutionary change in response to major environmental changes. (If you don't believe in evolution, you can jump to the next paragraph.) The same is true of this magazine's measurement regime, which we began in 1989. Every component is subjected to a standardized set of tests that remains the same for years. But occasionally, a new test device or my exposure to new thinking leads to rapid change.

Such was the case at January's Consumer Electronics Show, in Las Vegas, when I was discussing my measurements of digital products with MBL's chief engineer, Jürgen Reis. Many components these days offer users a choice of reconstruction filters; I have been characterizing these filters by showing first the impulse response, then the audioband frequency response, and then the spectrum of the product's output as it reproduces an equal mix of 19 and 20kHz tones, all with 44.1kHz data.

Reis suggested a test that would usefully display all the frequency-domain results in one graph: first decode a 44.1kHz-sampled high-frequency tone and perform a wideband spectral analysis on the product's analog output. This will reveal the presence of aliasing products, the so-called "negative frequencies" that I discussed in my 2011 Richard Heyser Memorial Lecture at the Audio Engineering Society's 103rd Convention. Then overlay that spectrum with that of the product reproducing 44.1kHz data representing white noise. This will unmask the nature of the filter's ultrasonic rolloff.

As I still had in-house the review sample of Arcam's FMJ D33 D/A processor ($3199.99), which offers a choice of three digital reconstruction filters, I used it to explore Reis's test. I used Stereophile's loan sample of the top-of-the-line Audio Precision SYS2722 system (see and the January 2008 "As We See It").

Fig.1 Arcam FMJ D33, impulse response with Burr-Brown filter (4ms time window).

The D33's default filter is a conventional linear-phase type, built into the Burr-Brown PCM1792 D/A chip. Fig.1 shows the D33's impulse response with this filter and 44.1kHz data. The ringing to either side of the pulse (one sample at 0dBFS) reveals this filter to be what is called a "half-band" type: the impulse actually maps the values of the digital filter's coefficients, and as these coefficients are symmetrical in time around the impulse, just a single set of coefficients needs to be stored on the chip.

Fig.2 Arcam FMJ D33, Burr-Brown filter, wideband spectrum of white noise at –4dBFS (left channel blue, right magenta) and 19.1kHz tone at 0dBFS (left cyan, right red), with data sampled at 44.1kHz (10dB/vertical div.).

Fig.2 shows the Reis test spectrum for this filter. With white noise, the response rolls off very rapidly above 21.5kHz, reaching the noise floor at 24kHz. The second and third harmonics of a 19.1kHz tone can be seen at –96dB (0.0015%) and –108dB (0.00033%), as well as some tones below –100dB in the audioband, the strongest of the latter lying at 13kHz. However, no aliasing products are visible between 22.05 and 44.1kHz.

Fig.3 Arcam FMJ D33, impulse response with Filter 1 (4ms time window).

Fig.4 Arcam FMJ D33, Filter 1, wideband spectrum of white noise at –4dBFS (left channel blue, right magenta) and 19.1kHz tone at 0dBFS (left cyan, right red), with data sampled at 44.1kHz (10dB/vertical div.).

Arcam's Filter 1 is a minimum-phase type, in which all the ringing occurs after the pulse (fig.3). The Reis test (fig.4) shows that it rolls off earlier than the Burr-Brown filter, just above 19kHz, and is down by 60dB at the Nyquist frequency (half the sample frequency). It is therefore an "apodizing" filter, and will remove the A/D converter's Nyquist ringing from the recording being played, resulting in improved sound quality. The same distortion and baseband spuriae are visible, but now an aliasing product at 25kHz (44.1 minus 19.1kHz) can also be seen, though this lies at almost –100dB (0.001%).

Fig.5 Arcam FMJ D33, impulse response with Filter 2 (4ms time window).

Fig.6 Arcam FMJ D33, Filter 2, wideband spectrum of white noise at –4dBFS (left channel blue, right magenta) and 19.1kHz tone at 0dBFS (left cyan, right red), with data sampled at 44.1kHz (10dB/vertical div.).

The D33's Filter 2 performs best in the time domain, with a single cycle of damped ringing (fig.5). However, the Reis test (fig.6) graphically reveals the price paid for this performance: the white-noise spectrum starts to roll off above 15kHz, then continues to roll off very slowly, reaching only 6dB down at the Nyquist frequency, and not dropping below the noise floor until 39kHz. As a result, the aliasing product at 25kHz lies just 10dB below the level of the 19.1kHz tone, and more aliasing spuriae have leaked into the audioband.

This test offers an easy-to-grasp picture of the effects of different reconstruction filters. I shall incorporate it into my testing regime.—John Atkinson

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