Upsampling. Truth vs Marketing

Eldartford's sentence: "In Sean's explanation the second set of 20 dots in set B should not be random. Those dots should lie somewhere between the two dots adjacent to them".

is exactly correct. One possible location of "somewhere between" could be legitimately the midpoint. There is no problem with that at all. If the waveform looks smooth then what's the issue with that??? How, in the world, do you know that the waveform at this point in the CD is not supposed to be smooth?? There could be a consistently low volume passage or a consistently loud volume passage of 1 particular instrument that creates a smooth area. Entirely possible.

Anyway, the thing to remember in your 2nd example is that when you placed that "random" set of points, you were looking at the output of the digital estimation filter. The output of digital estimation filter is very deterministic & it is designer created. The o/p simply cannot be random - no way!! It lies "somewhere between" the actual sampled data points off the CD along a line determined by the algorithm of the digital estimation filter. This is that (digital) filter that creates all those signature sounds (like Wadia's house sound, Sim Audio's, dCS's, etc, etc) that many love & equally many hate.

In Eldartford's example, I think, that he used a smooth waveform only to illustrate the point. This is the way that it is usually introduced in DSP 101 classes. His particular example is pertains to oversampling. When he shows the repeating of numbers, he has considered a 12X oversampling & when he does the div-by-4, he is considering 4X oversampling. The div-by-4 most probably represents the digital FIR that follows any over (or up) sampling operation.
My only question here is why did the example consider an oversampling of 12X then later decimate to 4X?? Should have just started of with a 4X DAC. Anyway.....

You mentioned "error correction" for the 2nd time. Error correction in redbook CD playback has nothing to do w/ upsampling or oversampling. Error correction is NOT designed to correct the music written on the CD. It is designed to compensate for high-speed read & transmission of the bits where read errors will occur (owing to the high speed read operation). I think Eldartford's succinct explanation is exactly what error correction is all about. Any other idea of it is a mistaken impression.

I have read the recent upsampling verbose text by Moncrieff on IAR. IMHO, I have not read more bull**** anywhere that filled up so many pages. Very little of what he has written is correct. AFAIK, Moncrieff is very lost when it comes to up & oversampling. If you are taking your lessons from him, then I can see why you are mistaken too. Get hold of a DSP text (like Oppenheim & Schaeffer or Rabiner & Gold) & read that. You'll get the correct explanation of upsampling & oversampling.

Sean...The sampling (your first set of dots) is at 44.1KHz. The highest audio information that exists at this sampling rate is around 20KHz, and at this frequency the music signal amplitude is very small. Therefore, unless the signal is momentarily a constant (two adjacent points the same) the in-between points will lie between adjacent points. Of course this is all overlaid with random noise that will blur the quantization staircase.

The CD recording protocol has been cited as an everyday example of the application of CRC error correcting technology, and I have seen descriptions of the CD protocol as having interpolation as a "fall back" procedure when the CRC error correction fails. Of course the second "fall back" is to abort playing the disc, and this ought to be the only time that the process is easily heard.

To tell the truth I have never actually read this infamous "Red Book" which defines the CD spec, and so am relying on what others have reported. How would I get a copy?

Bombaywalla...Your check is in the mail :-)

Sean....Homework is to read.. http://en.wikipedia.org/wiki/Reed-Solomon_error_correction
Test on Monday :-)

Sean, in fact, Jeff Kalt of Resolution Audio was marketing and using "upsampling" in his players at the time, so yes I do think some manufacturers will be honest when asked directly.

But more to the point, what do you think is so magical about 96kHz or 192kHz? Why not 88.2 or 176.4 or 352.8? I think the obvious answer is that the high rez format in DVD-A is either 96kHz or 192kHz...marketing anyone??

If you could, would you please contrast your upsampling dot graph with the equivalent oversampling dot graph? Remember that to get to 96kHz from 44.1kHz in your example you have to increase the number of dots from 20 to 43.5 dots. What you described is essentially a 2x oversampling routine with linear interpolation. The graph cannot get any smoother than the original unless you use something other than linear interpolation. Yyou are just connecting a series of dots in a line between samples, otherwise.

The main reason for adding points between the original samples is ultimately allow a more gentle analog filter. The original (really bad souding) CD players used no oversampling and analog brick wall filters to avoid the problems associated with the Nyquist limit for 44.1kHz sampling (22.05kHz) and the spurious images that get reflected back in band. These sounded horrible and led to 2X, 4X, 8X etc oversampling moving these images well beyond the audio band and allowing more gentle (better sounding) analog filters.

To paraphrase Charles Hansen, adding another digital filter (upsampling) to the chain will affect the sound; however it is certainly possible to design a single digital filter with exactly the same composite characteristics as the two cascaded filters, usually justs costs a little more money.

Anyway, not trying to be a pain in the a$$, I just think the marketing component of the choice for 96kHz or 192kHz needs to be pointed out.