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Technology, Theory and Design

Poking a Round Hole in a Square Wave

One of the most intriguing aspects of a professionally-focused event like Surround 2002 is the opportunity it affords to hold up marketing claims to more rigorous scientific scrutiny than one finds in consumer-oriented forums. Case in point: a potential giant-killer presentation by Craig Anderson of Craigman Digital, in which the DVD-Audio technical consultant to Warner/Elektra/Atlantic raised questions about the oft-touted superior accuracy and precision of Direct Stream Digital over PCM.

Click for a Larger Image

Anderson said he became intrigued when he recently saw the “square-wave reproduction” comparison frequently touted by Super Audio CD format co-developer Philips Electronics in its SACD promotional literature (2.4Mb Adobe Acrobat PDF download taken from the Philips SACD web site). The Philips example shows a graph of a 10kHz square wave passed through a DSD analog-to-digital-to-analog chain, compared with the same signal passed through a PCM A-D-A process; the DSD graph cleanly reproduces the square silhouette of the source, while the PCM path yields a rounded sine wave.

While the intent of the graphic is to persuade readers that DSD-based SACD is superior to the PCM-based DVD-Audio format, the comparison struck Anderson as being deceptively simplistic in several respects. As a specialist intimately familiar with the sonic attributes of PCM, Anderson recalled, “I knew that at lower sampling rates a 10kHz square wave would look pretty shabby, but the output of the PCM converter seemed way too sinusoidal for high resolution PCM [i.e., at DVD-Audio resolutions].” The other thing that aroused his curiosity, he said, “was the cleanliness of the DSD graph. It looked nearly identical to the square wave – not nearly shabby enough, I thought.”

To test the Philips claim, Anderson duplicated the comparison, armed with an analog 10kHz square wave generator, a dCS A/D converter, a dCS D/A converter, a good old-fashioned analog oscilloscope, and a digital camera (to capture the output of the oscilloscope). First, he ran a 10kHz signal directly through the oscilloscope to obtain the baseline graph shown in Figure 1 (right).

Figure 1 - Click for a Larger Image

Next, he ran the same signal through the PCM converter at sample rates of 44.1kHz, 96kHz, and 192kHz. As expected, at its lowest resolution of 44.1kHz (the sample rate of standard CDs), PCM yielded the sine wave shown in Figure 2 (right). Anderson said he did not consider this surprising, since at 10kHz, a CD takes only 4.4 samples per cycle. “Filtering and interpolation smooth out what would otherwise be a rather jagged signal, thereby accounting for the rounded graph,” he explained.

Figure 2 - Click for a Larger Image

However, since the Philips literature had specifically referenced DVD-Audio in its comparison, Anderson next examined the PCM output at DVD-Audio’s higher resolution sample rates. Here, the graphs told a very different story. The 96kHz trace (shown in Figure 3, right) improved in rise time, resulting in a sustained peak duration much closer in appearance to a square wave.

Figure 3 - Click for a Larger Image

Anderson explained that the bump at the peak’s extremities is the signal’s first harmonic, now identifiable thanks to the increased sampling precision. At 192kHz (Figure 4, right), Anderson reports, the trace improves even more, cutting the rise time in half and revealing the square wave’s third harmonic.

Figure 4 - Click for a Larger Image

Turning to the DSD trace (Figure 5, right), Anderson found that “The DSD trace does look very similar to the picture in the Phillips brochure, and represents the square wave better than the first two PCM traces [at 44.1 and 96 kHz].” But when compared with 192kHz PCM, DSD performance proved very similar.

Figure 5 - Click for a Larger Image

Overlaying the DSD and 192 kHz traces (Figure 6, right), Anderson pointed out that the difference in rise time between DSD and 192 kHz are “statistically (and perhaps audibly) insignificant.” Also, both accurately extract the first and third harmonics from the square wave. However, Anderson noted one readily apparent difference between DSD and the highest resolution PCM – the DSD trace is blurry.

Figure 6 - Click for a Larger Image

The DSD trace, Anderson points out, is tainted by DSD’s dirty little secret: the excessive amount of noise created by one-bit sampling. To disguise it, Sony and Philips implemented a noise-shaping system that shifts noise from the lower frequencies into the ultrasonic range, where it is presumably inaudible (a debatable point in itself, Anderson maintains).

However, Anderson attributes the primary cause of the DSD “blurring” shown in Figures 5 and 6 to imprecise traces along the vertical and horizontal axes, which are much more significant than any noise superimposed on the traces themselves. He suggests these imperfections in the DSD signal are evidence of imperfections in amplitude and time domain, respectively. “Were one to zoom in on the DSD signal,” he said, “one would actually see amplitude fluctuations of 50% peak amplitude, and time domain errors similar to the 96kHz rise time deviation. The defect, when compared with the PCM photos, illustrates perfectly the reason that DSD is incapable of reproducing the same transient twice.”

What can we draw from these findings? Anderson was quick to point out that a square wave is not the most pleasurable or representative musical experience (as anyone who’s ever heard one can readily attest). However, it does provide a “torture test” yardstick. In testing one of the DSD proponents’ key marketing claims, Anderson concluded, “We can clearly see that with this particular waveform, PCM produces a much more faithful copy of the original with both accuracy and precision. It does help dispel the myth that DSD’s one-bit sampling is the panacea to the world of digital audio.” [Philip Brandes]


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Show report last updated: 2nd February 2003.

 

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