SIGNALS & NOISE (Letters to Editor) (Jul. 1991)

Reprise of the Bitstream

Dear Editor:

We at Analog Devices -- as leading suppliers of audio converter ICs--are pleased to see in-depth articles on converter technology such as "Music of the Bitstream" by Prasanna Shah (January). Because of the debate (and confusion) in the industry between oversampled sigma-delta converters and "classical" current-steering converters, his article was timely and informative.

Unfortunately, Shah's article continues to reinforce widespread confusion about the role of "oversampling" in the digital-to-analog conversion process. The first point to be made is that digital oversampling interpolation filters are required regardless of the D/A converter technology. That is, both oversampled and current-steering D/A converters are preceded by interpolation filters in virtually all modern designs. Confusion is natural when trying to understand why a sigma-delta D/A converter that is oversampled by 64 is preceded by an interpolation filter that oversamples by eight. There are two kinds of oversampling going on. The former is accomplishing quantization noise shaping, as is well explained in Shah's article. The latter, interpolation filtering, "... allows for simpler and lower order, phase-linear analog post filtering," as reported. In fact, that's the only reason for interpolation filtering; its other consequences are negative.

What oversampling interpolation filtering does is move the Nyquist "images" of the audio signal to higher frequencies. Without an oversampling interpolation filter, the first image at a 44.1-kHz sampling rate will begin to appear around 24 kHz. High-order, "brick-wall" analog filters would be required to eliminate these images--with nasty audio consequences, as the first-generation CD players demonstrated. Both oversampled and current-steering D/A converters will produce these Nyquist images starting around 24 kHz unless preceded by an interpolation filter. If the interpolation filter oversamples by four, the first image will occur near 176.4 kHz; if by eight, near 352.8 kHz.

Shah really muddies the waters by adducing two additional but fallacious "reasons" for oversampling interpolation filtering: (1) "To reduce the quantization noise in the analog audio bandwidth" and (2) "To improve the signal-to-noise ratio (S/N)." The phrase "quantization noise" is ambiguous, and Shah fails to clarify. There are three sources of quantization noise in the conversion chain if a sigma-delta D/A converter is used, two if a current steering type is used. The first is the quantization noise from the analog-to digital conversion done in the recording process. There is nothing playback equipment can do about recording quantization noise once it's on the CD! No electronic magic can take away noise the studio introduced or improve the ratio of signal to this noise. Shah's argument about smaller step sizes with interpolated data is completely irrelevant to reducing the noise introduced by the original 16-bit quantization process. Even ideally, this noise is ± 1/2 least-significant bit at the 16-bit level.

Sigma-delta D/A converters introduce their own quantization noise, but eliminating that noise source is what noise shaping is all about; interpolation filters have no impact on that noise. The third type of quantization noise is ironically introduced by the interpolation filter itself. Shah is correct that oversampling reduces this noise, but it's noise that wouldn't even be there without (oversampling) interpolation.

Interpolation filters perform multiplication/accumulation operations on 16 bit input data. To retain "perfect" accuracy using 16-bit coefficients requires internal accumulators that are at least 32 bits wide. Ultimately, the filter outputs a 16-, 18-, or 20-bit word that represents a signal "interpolated" between the original signal values. In any event, accuracy is lost when the filter's internal values are truncated to one of these smaller word widths. This quantization noise is probably best called "requantization" noise because truncation effectively accomplishes a second quantization of the music signal. (The finite word length of the coefficients, non-ideality of the digital filter, and other factors also contribute digital noise to the interpolation process, but in a well-designed interpolator, truncation noise will dominate.)

Now, it's easy to explain the benefits of 18- and 20-bit D/A converters. Re-quantization noise will be spread out over the wider frequency range of the interpolation filter's oversampling rate. If the interpolation filter's results (at eight-times oversampling) were truncated to 16 bits, the requantization noise would add about 1.5 dB to the noise floor. If instead we truncate at 18 bits, then the requantization noise is lowered by about 12 dB. Truncation at 20 bits reduces requantization noise yet another 12 dB. Thus, the advantage of 18and 20-bit converters is that they can reduce the deleterious effects of interpolation filters to a fraction of a dB above the theoretically ideal. Whether this noise difference is audible above all the other noise sources in the playback chain is a question I'll leave to the "golden ears."

David Fair; ASIC Marketing Manager; Analog Devices; Wilmington, Mass.

Author's Reply: I don't think there is any confusion about the role of oversampling in the digital-to-analog conversion process. Neither does the article associate oversampling and interpolation filters only to a specific D/A converter technology. It is common knowledge that oversampling and interpolation filters have been utilized since 1982, when the 14-bit D/A converters were used. It seems to me that Mr. Fair is mixing up the roles played by the oversampling process and interpolation in the reconstruction of the audio signal. It can be easily found in almost all elementary textbooks on digital signal processing that the quantization noise is proportional to the step size. If 1 is the step size, then the quantization noise will be (1/12) Δ².

Also, the article never claims to reduce the quantization noise introduced by the original digital master recording in 16 bits, through either D/A converter technology. In fact, the article tries to dispel the myth about 18- or 20-bit accuracy being achieved in sound reproductions of 16-bit-mastered Compact Discs using the 18- and 20-bit D/A converters, which is perpetuated by the manufacturers of these converters and the CD players that employ them.

Lastly, Mr. Fair is trying to explain the benefits of 18- and 20-bit D/A converters. He is unfair in associating the extra bits in the 18- and 20-bit converters with the spreading of requantization noise over a wider frequency range. The smaller step size in voltage levels does not spread the noise in frequency. But a noise shaper with oversampling and interpolation will shift the quantization noise from the audio spectrum to higher frequencies. I recommend the fourth reference listed at the end of the article for further information on this topic.

In order to have any kind of benefit from 18- or 20-bit D/A converters, they need to maintain less than 1/2 LSB differential linearity, 1/2 LSB integral linearity, minimal gain and offset errors, minimal glitch energy, and minimal zero crossing distortion--and to keep these parameters constant-over the entire operating temperature range. I am sure that even Mr. Fair will agree that such an 18- or 20-bit D/A converter is not commercially available, and even if it were, it would not be viable for consumer CD players.

-Prasanna Shah

An Alternative Bandwagon

Dear Editor:

I was highly delighted and a little surprised to see reviews of Mano Negra's Puta's Fever and Tackhead's Friendly As a Hand Grenade in your November 1990 issue. I've always enjoyed the reviews in the Rock/Pop Recordings column, but seeing these "alternative" bands was great! I hope this turns into a trend. There's quite a bit of alternative music out there, and a lot of it is very good. There just doesn't seem to be enough exposure, but if a few more avenues of exposure open up, we'll be hearing more of this music on the mainstream stations and more will be available in mainstream stores. And this would suit me just fine.

-Marty P. Hoar; Longmont, Colo.

Shining Sunier

Dear Editor:

John Sunier's interview with the rather incredible Robert Parker and his infernal machines (February 1991) was absolutely first-rate. Best piece you guys have run in months. Three cheers for all concerned from sun-drenched La Jolla.

-J. Lee Anderson; La Jolla, Cal.

More Like Oil and Vinegar

Dear Editor:

In response to a letter in your January 1991 issue from Leland A. Beaman:

YES, Audio is an outstanding magazine.

NO! Audio should not eliminate the wonderful world of video from this outstanding publication.

While I agree the field of audio deserves its own literature, video products are taking a great part in the audio systems of many of the readers of Audio magazine.

The two are not oil and water.

Part of what makes this hobby so exciting is that every year, if not every day, something new and different is introduced to us. From the movie theater we now have surround sound in our homes that works in harmony with our audio media and our video media.

We no longer live in an age where a television is for seeing and not hearing.

In my system, the two work quite well together.

Also, I feel a bit sorry for Mr. Beaman, as it seems he must not have yet experienced the joy of recording audio onto Hi-Fi videotape. It would probably blow his current "audio" cassette deck out of the water.

Grant M. Billings; Milwaukee, Wisc.

Referral of Fortune

Dear Editor:

I would like to tell you about a remarkable experience with one of your advertisers, Advanced Audio in Leechburg, Pa. I had written to them looking for a couple of cheap woofers for my workshop and mentioned that I intended to use the woofers with small speakers I had on hand from a junked car stereo.

Advanced Audio wrote back, explaining that none of their speakers were exactly what I needed. Instead, they provided the name of a different company, a list of exactly what to order, and precise diagrams for building the enclosures and hooking up the crossover. If they did all this for somebody who wasn't buying anything, their paying customers must really be treated like royalty.

-Jon Vilhauer; Placerville, Cal.

(Source: Audio magazine, 07/1991)

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