Noise, Modulation, & Digital/Analog Conversion
The technique is straightforward: drive the digital converter with the code representing a low-frequency sinewave, high-pass filter the converter's output to remove the test signal, and perform a 1/3-octave spectral analysis of the converter's output. The result is plotted as noise level vs frequency. The measurement is repeated at different input-signal levels, with each curve overlaid on the previous curves for easy comparison.
The test-signal frequency is 41Hz, chosen because it is not an integer sub-multiple of the sampling frequency. The test signal will thus exercise the greatest number of steps in the DAC. Five signal levels are used, from -60dB to -100dB (referenced to full scale, designated -60dBFS and -100dBFS) in 10dB steps.
Basically, the technique measures noise-floor shifts (a result of quantization distortion) as a function of signal level. There is a direct correlation between low-level linearity and performance in this test. In addition to how much the noise floor is modulated by signal level, the measurement reveals shifts in the noise floor's spectral balance with changes in signal level. Ideally, the noise-floor spectrum should remain constant with level, producing curves that exactly overlay each other. Psychoacoustic research by Louis Fielder at Dolby Labs (those guys know something about noise-floor modulation!) indicates that noise-floor shifts of 2dB are audible. Further, Dr. Cabot's paper asserts that the ear is very sensitive to shifts in the noise floor's spectral balance; changes on the order of 1dB are reportedly audible.
Armed with that introduction, here are the results of this measurement technique, performed on six digital processors. I've reviewed all six units and know their sonic signatures well; it thus may be possible to correlate the measurement results with listening impressions. For background, their prices and internal D/A converters are listed here: 1) Audio Research DAC1-20, $3495, UltraAnalog 20-bit DAC; 2) PS Audio SuperLink, $1195, dual Burr-Brown PCM61PK DACs; 3) Meridian 203, $990, two Philips 7321 Bitstream DACs used in "dual differential" mode; 4) Kinergetics KCD-55 Ultra, $3995, two UltraAnalog 20-bit DACs used differentially; 5) Wadia 2000, $7450, four unknown R/2R ladder DACs fed time-shifted signals; 6) Mark Levinson No.30, $13,950, two dual UltraAnalog 20-bit DACs used differentially.
Fig.1 is the DAC1-20. Compared to the plots Dr. Cabot shows in his paper on typical 14-bit converters, the DAC1-20 is superb. There is very little change in either the noise floor's level or spectral balance with input level, indicated by how closely the curves are bunched together.
Fig.1 Audio Research DAC1-20, noise modulation, -60 to -100dBFS
The SuperLink is shown in fig.2. The noise floor is intrinsically much higher than the DAC1-20, and there is a substantial change in the spectral balance as a function of input level, especially in the octave between 10kHz and 20kHz. Further, the spectral balance of the SuperLink's noise floor is radically different from the DAC1-20. In the two octaves between 300Hz and 1.2kHz (extremely important musically), the SuperLink has about a 13dB higher noise floor. At 10kHz, it is only about 7dB higher than the DAC1-20.
Fig.2 PS Audio SuperLink, noise modulation, -60 to -100dBFS
Fig.3 shows the Meridian 203's performance on this test. The curves look almost as good as the DAC1-20, but have more variations with level, especially between 1kHz and 6kHz. This is the only 1-bit converter of the group (and the least expensive) (footnote 2).
Fig.3 Meridian 203, noise modulation, -60 to -100dBFS
Next up is the Kinergetics KCD-55 Ultra (fig.4). Although the Ultra uses UltraAnalog 20-bit DACs, its noise floor was about 10dB higher than the DAC1-20's. It has, however, an identical spectral balance, and similarly good groupings of the curves.
Fig.4 Kinergetics KCD-55 Ultra, noise modulation, -60 to -100dBFS
The venerable Wadia 2000 is seen in fig.5. This enigmatic converter exhibits poor bench performance (at least on standard tests), yet is superbly musical. As can be seen, there are very large variations in the noise floor as a function of input level, indicated by the loose grouping of the curves. In addition, there are severe shifts below 1kHz, with one input level producing a 10dB increase in the noise floor at about 500Hz.
Fig.5 Wadia 2000, noise modulation, -60 to -100dBFS
Finally, the No.30 (fig.6). This was the best-measuring processor in this test, with the lowest noise floor and very little spectral-balance change with input level.
Fig.6 Mark Levinson No.30, noise modulation, -60 to -100dBFS
To give you an idea of the quality of converters found in professional digital multitrack recorders, take a look at fig.7, reprinted from the AES paper. Besides having a high intrinsic noise level, the shifts in the noise's spectral balance are huge.
Fig.7 Noise modulation of one channel of digital multitrack recorder, -60 to -100dBFS
What does all this mean? I'm not sure. From this small sampling, I saw no correlation with listening impressions. We will, however, continue measuring digital converters with this technique in the hope that some trend may emerge in the long run (footnote 3). Any attempt to relate measurement to subjective evaluation is a step in the right direction.
Footnote 1: "Noise Modulation in Digital Audio Devices" is available for $3 from the Audio Engineering Society, 60 E. 42nd Street, Room 2520, New York, NY 10165-0075. Tel: (212) 661-8528.—Robert Harley
Footnote 2: The Meridian 203 was apparently revised at the end of 1991 to incorporate Philips's latest "DAC-7" Bitstream converter. It keeps the 7321, however, to make use of its digital low-pass filter, which Meridian's Bob Stuart feels to produce the lowest modulation noise. RH's sample of the 203 was the earlier version.—John Atkinson
Footnote 3: Stereophile's reviews of digital products included noise-modulation measurements through the end of 1997. After that, we stopped routinely publishing the results as this test only revealed problems where the linearity error and undithered low-level tests had already shown that something was wrong with the DAC design or implementation.—John Atkinson