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Hmmm...

Todd:

I think there might be a little misunderstanding here...

I use system as the most generalized expression of the complete AD, storage and DA activities. Dither can be applied or not as part of that system.

I was asking about the distortion characteristics of dithered versus undithered digital recording (at low levels).

Your post included:
Peter: "Are all harmonics present in equal quantities?"
Todd: No. And I cannot think of a condition in audio where the answer would ever be "yes."

See the link below for a real-world example of exactly this.

You also said:

The distortion indeed increases, but "similar levels at all harmonics" is not really the case, because no distortion contains harmonics that are remotely close to such character or consistency.

Im not sure I understand what you're trying to say. Are you suggesting that no examples of distortion show a consistent pattern, or are you referring only to digital processing?

Any occurence of harmonic distortion (in any system) will have an envelope that describes the relative amplitude of the harmonics. In most cases that envelope changes shape as the level is raised or lowered. Simple systems (think SE amps) tend to have a distortion spectrum that is dominated by low order harmonics, AND decreases monotonically with level. The lower the level, the lower the %age distortion. Other systems (think Class B amps) have a different characteristic; as the level is lowered, there is a point at which the distortion begins to rise.

Some systems exhibit differing behavior for even vs. odd harmonics, such as push-pull circuits.

I am curious about the distortion-vs-level behavior of Redbook CD (viewed as a whole sytem).

Here's my understanding:

As the signal level drops in a digital system, the number of bits used to encode the signal drops. Think of a simple sine wave. When you get down to v.v. low levels, say 2-bits, the sine wave is being stored digitally as a signal with only 4 discrete levels. When this signal is converted back to analog, it will have spectral components at multiples of the original sine wave's frequency. In other words, harmonic distortion.

In a thread over on the vinyl asylum, John Elison posted a spectrum of a -60dB 1kHz signal (16/44.1) that had 2nd - 5th harmonic distortion levels of 0.126%, 0.398%, 0.112%, and 0.2%. I have linked it below. These numbers suggest a pattern something like: each harmonic is at roughly the same level, except that even harmonics are lower than odd. John listed the distortion components out to the 10th, and they were all within a few dB of one another.

What I wanted to know is whether this is predicted by the mathematics of the A-D process.

Later in the same thread, another poster (Werner) pointed out that the signal was probably undithered and that dithering would eliminate these harmonic distortion components. That's what I'm trying to determine.

Does that clarify anything?

Peter





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