Notes from selected Web sites:
Uwe Beis writes about delta sigma encoding on SACDs: "The whole system from the analogue input to the analogue output now requires only one modulator and one low pass filter instead of two, each with conventional digital recording. Please remember: The bitstream of modern, high quality ADCs and DACs use an oversampling rate of 64, e.g. the amount of data is 64 bits for each audio sample - compared to 16 or up to 20 or 24 of conventional bits required for a comparable quality. Technically, SACDs are DVDs and based on a sampling frequency of 2.8224 MHz (= 2.8224 MBits net per channel). Not that much more than on audio CDs (0.7056 MBits net per channel), and no problem at all for a DVD with its high capacity."
Digital Dharma of Audio A/D Converters (1997) offers this explanation (excerpt): "Essentially a delta-sigma converter digitizes the audio signal with a very low resolution (1-bit) A/D converter at a very high sampling rate. It is the oversampling rate and subsequent digital processing that separates this from plain delta modulation (no sigma). [Regarding] quantizing noise it is possible to calculate the theoretical sine wave signal-to-noise (S/N) ratio (actually the signal-to-error ratio, but for our purposes it's close enough to combine) of an A/D converter system knowing only n, the number of bits. Doing a bit (sorry) of math shows that the value of the added quantizing noise relative to a maximum (full-scale) input equals 6.02n + 1.76 dB for a sine wave. For example, a perfect 16-bit system will have a S/N ratio of 98.1 dB, while a 1-bit delta-modulator A/D converter, on the other hand, will have only 7.78 dB! . . . . One attribute shines true above all others for delta-sigma converters and makes them a superior audio converter: simplicity. The simplicity of 1-bit technology makes the conversion process very fast, and very fast conversions allows use of extreme oversampling. And extreme oversampling pushing the quantizing noise and aliasing artifacts way out to megawiggle-land, where it is easily dealt with by digital filters (typically 64-times oversampling is used, resulting in a sampling frequency on the order of 3 MHz). To get a better understanding of how oversampling reduces audible quantization noise, we need to think in terms of noise power. . . . With oversampling the quantization noise power is spread over a band that is as many times larger as is the rate of oversampling. For example, for 64-times oversampling, the noise power is spread over a band that is 64 times larger, reducing its power density in the audio band by 1/64th."
- Christopher Hicks states that "by using some digital signal processing, the stream of 16-bit words at 44.1kHz can be transformed to a stream of shorter words at a higher rate. The two data streams represent the same signal in the audio band, but the new data stream has a lot of extra noise in it resulting from the wordlength reduction. This extra noise is made to appear mostly above 20kHz through the use of noise-shaping, and the oversampling ensures that the first image spectrum occurs at a much higher frequency than in the multi-bit case. This new data stream is now converted to an analogue voltage by a DAC of short word length; subsequently, most of the noise above 20kHz can be filtered out by a simple analogue filter without affecting the audio signal." (This statement was formerly posted at a site called RecAudioPro, www.vex.net/~pcook/RecAudioPro/digital.html, not accessible in September 2006.)
- In September 2005, the Wikipedia entry for Direct Stream Digital reported "There is much debate over whether DSD or PCM is ultimately the better digital encoding format, as can be seen in the format war between SACD and DVD-Audio. The DSD technology is pioneered by Ed Meitner, an Austrian sound engineer and owner of EMM Labs. It is now developed by Sony and Philips, the initial starters of the audio CD."
- Good introductory information at Direct Stream Digital (DSD) Encoding includes this fact: "Using single stage FIR [finite impulse response] digital filtering and noise shaping, 1-bit DSD can be down-converted into standard 24, 20 or even 16-bit PCM audio for CD distribution while still retaining the maximum possible audio quality. The system's 2.8224 MHz sampling rate is specifically designed for high precision down-conversion to all current PCM sampling rates using simple integer multiplies and divides."