Super Audio CD: The Rich Report Page 2
In delta-sigma DAC designs the trend has been to go to 20 or more levels for the internal DAC instead of one level, and up to 18-bit linearity (Analog Devices, Crystal, and even single Bitstream inventor Philips Semiconductor). An advanced technique that randomizes a multibit DAC's linearity errors by shuffling the DAC elements around for each code conversion has been universally employed for high-end converters. Oversampling rates of 128x are now universally used for the highest-performance DACs, as they were in the ADCs. Burr-Brown continues to use full 20-bit sign-magnitude DACs for its highest-performance products, but these products use no feedback, instead relying on analog matching techniques to achieve the desired linearity.
In terms of information theory, a delta-sigma stream can be shown to carry less information than a linear PCM stream of the same bandwidth/noise-floor product (footnote 4). It makes sense, therefore, to convert the bitstream output by a delta-sigma ADC to an LPCM stream before it is sent to a storage medium. In digital signal-processing, the circuit block that converts a high-speed low-bit datastream—output, for example, by an ADC—to a low-speed, higher-bit stream, is called a decimator. The decimator reduces the total number of data bits per second (bit depth times the sampling rate) coming from the ADC. Thus the decimator changes the inefficient delta-sigma stream from the ADC to the efficient PCM stream. (In the case of 24/96 DVD-A, this is 2.3 megabits per second per channel (footnote 5).
The equivalent DSP block in a DAC design is called an interpolator; it converts the incoming low-speed multibit stream to a higher data rate to drive a delta-sigma DAC. In effect, the efficient PCM stream is turned into the inefficient delta-sigma stream, which runs at a higher rate of total bits per second. Remember, the reason we create a delta-sigma stream is because it is cheap and easy to make DACs and ADCs that have low resolution but that run very fast with inherently good linearity. It is difficult and expensive to make lower-speed, higher-resolution converters that work directly on the PCM stream. This is the only reason for the existence of the inefficient delta-sigma stream.
With 0.12µm CMOS integrated-circuit technology, well-designed interpolators and decimators are so small they cost almost nothing. However, note that I said "well-designed." All the digital arithmetic must be properly done, including data-rounding and addition of dither. Internal data paths and filter coefficients must be as wide as necessary to ensure that no nonlinearities are introduced.
Please note that it is possible to build a decimator or interpolator that can distort the signal. Properly designed decimators and interpolators are audibly transparent, but improperly designed ones can introduce audible errors. I have little doubt that low-end digital filters/interpolators in some CD players are cheapened enough to cause audible problems. But bad design must not be confused with a fundamental problem in the concepts of decimation and interpolation.
With Super Audio CD, Sony and Philips offer a product that encodes the inefficient high-sample-rate, low-resolution bitstream. The Direct Stream Digital (DSD) encoding used on SACD is nothing more than the raw bitstream output by a seventh-order delta-sigma A/D converter. DSD uses only a single bit to encode the signal, whereas the high-performance ADCs from all leading manufacturers—and all work in advanced research—use three codes, and in many cases more than that. Significantly, the Sony/Philips DSD system oversamples only at a 64x rate (relative to 44.1kHz). That's half the rate used in all high-performance ADCs and DACs available today. To get better than 20-bit performance below 20kHz with a 1-bit stream, a seventh-order modulator must be used at this low oversampling rate. The higher the modulator order and the lower the number of levels, the more difficult it is to remove the high-frequency energy of the 1-bit quantizer. The problems made worse include sensitivity to clock jitter and matching of clock edge rise and fall times. Aliasing of out-of-band noise into the passband becomes more difficult to deal with in a high-order, single-bit system.
The one-bit encoding and 64x oversampling rate results in a data rate of 2.8224MHz per channel for DSD, which looks similar to 24/96 LPCM's rate of 2.3Mb/s. Remember, however, that DSD uses an inefficient delta-sigma bitstream. If we look at the theoretical spectrum of a full-scale, DSD-encoded 1kHz tone (fig.1, after Sony), we see that the 24-bit performance is not achieved in-band, and that the S/N ratio drops quickly above 20kHz as the quantization energy from the 1-bit coder becomes significant. The 24/96 LPCM used on DVD-A offers 24-bit noise and distortion performance all the way up to 46kHz.
Fig.1 DSD encoding, spectral analysis, DC-200kHz, 1kHz tone at 0dBFS (log. frequency scale, FFT bin width 10Hz). After Sony.
Because DSD uses a high-order delta-sigma modulator, the noise above 20kHz rises very quickly. (The higher the order, the faster the rise.) To prevent high levels of high-frequency energy from getting out of the player, an analog low-pass filter at 100kHz is required during SACD mastering. Even so, a large amount of out-of-band noise might be passed on to the power amplifier, perhaps as high as a tenth of the full power output of the system. If not rolled off by the amplifier, this may be just below the energy level to harm a tweeter. This is why SACD players are required to use a further 50kHz low-pass filter on their outputs (though this can be defeated). The need for these low-pass filters works against claims that DSD has wide bandwidth and low phase shift.
Footnote 4: See Malcolm Omar Hawksford, "Bitstream versus PCM debate for high-density compact disc."—John Atkinson
Footnote 5: For five channels of 24/96 data, this results in a total data of 11.5Mb/s, which is higher than the maximum possible rate that can be retrieved from a DVD. The DVD-A specification allows this rate to be reduced either by encoding the rear channels at a lower sample rate, or by using Meridian Lossless Packing (MLP). MLP takes advantage of the correlation between samples with music data to reduce the amount of data encoded on the disc. Unlike lossy compression schemes, such as Dolby Digital, or DTS at the lower rates, the PCM data packed with MLP can be retrieved with no loss of information.—John Atkinson