Upsampling. Truth vs Marketing

You guys are all correct. Where i "fell down" on this one was that i was thinking in the analogue realm rather than in the digital realm. When i was thinking of how to explain "upsampling", i was trying to demonstrate exactly how "non symmetrical" a musical waveform really is. This is why i suggested that the second set of 20 dots / samples be placed randomly rather than in a neat and orderly fashion between the other dots / sample spaces.

What i forgot to take into account was that we weren't dealing with analogue here at all. We are dealing with analogue that has been hacked to bits ( literally ), completely butchered as it was converted into another format and is now trying to be re-assembled as best possible back to what it was originally. Kind of like taking a fish, throwing it into a blender and hoping to re-build the fish once it comes out of the blender. Good luck.

If you doubt this, try looking at some of the waveforms that Stereophile tries to reproduce on various digital devices. Given that these are symmetrical test tones, you can only imagine how poorly some of designs / devices would do with more dynamically complex musical signals fed into them.

As such, there is little resemblance to what the original analogue waveform looks like after digital processing due to a LOT of various factors, some of which have been more than amply pointed out above. I apologize for the mistake and would like to say "Thank You" to those that corrected my mistakes.

Having said that, i'm glad that at least part of what i was trying to convey was understood and not completely lost. To be specific, i'm talking about the various types of filtering and cut-off frequencies used, why this area of operation affects what we hear inside the audible bandwidth, etc...

As to Germanboxer's comments, i agree that the majority of upsampling is based on parts that are already commercially available products. This not only makes things easier to design, it is also cheaper to produce. Otherwise, manufacturers would have to build "one off" devices for each product manufactured, which would make every upsampling DAC a custom built piece. While this would probably result in better quality as everything would be designed from the ground up rather than just using what was already available, it would also be horrendously expensive to produce, especially in very small quantities. By relying on parts / circuitry that is already in production, at least a portion of the benefits of such an approach can be had and prices kept within the "working man's" budget. Even then, some "working men" may still have a problem with the price on some of these units. Sean
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Not quite, Eldartford. A digital system cannot accurately reconstruct a wave that is exactly half the sampling frequency. That's why I said the sampling rate had to be fractionally higher (granted, a very tiny fraction) than twice the highest frequency. In the example given, there were exactly two samples per cycle, and that wouldn't work.

And just what is it you think is "the biggest problem with redbook CDs"?

Germanboxers,
basically, you are correct in pointing out that 96K & 192K were selected owing to other hi-res audio formats (namely DVD-A). Here the electronics is a multi-rate system wherein it up/oversamples by 160 & then decimates by 147 to change the sampling rate to 48K from 44.1K.

However, if you buy any of SimAudio's products, then you'll find that they oversample at exactly 8X, which is 352.8KHz!!! So, here is one commercial co. that doesn't use 96K, 192K or 384K. There must be others too but I cannot think of them right now.
FWIW.

Pabelson...I guess you mean that if the sine wave frequency is EXACTLY one half the sampling frequency, a sync situation exists. OK. Change the sampling frequency enough so that the phasing of the sine wave drifts across the sampling interval. Picky, Picky :-)

I personally don't have much of a gripe about CDs, but then my ears are 67 years old, and don't have the HF sensitivity of some of our golden eared friends. Based on my experience, which led me to believe that Nyquist was an optimist, I can believe that HF is a lot better with 96KHz sampling.

Sean...I disagree about the effect on quality of "off the shelf" parts. In the military electronics business, we used to design all our own chips, even microprocessors. However, even at great expense we could never match the research and development effort, propriatary skill, and quantity production, typical of commercial products that were functionally equivalent to our designs. A mature "off the shelf" product has had all its bugs weeded out.

Since Sean has confessed his error, I will do the same. My explanation actually showed a ramping signal of 3 units in four samples. While this was not incorrect, it is not consistent with the analog signal that I assumed at the beginning. The following is an updated version of my explanation, for posterity.

Phillips used 4 times oversampling in their first CD players so that they could achieve 16 bit accuracy from a 14 bit D/A. At that time, 16 bit D/A, as used by Sony, were lousy, but the 14 bit units that Phillips used were good. The really cool part of the story is that Phillips didn't tell Sony what they were up to until it was too late for Sony to respond, and the Phillips players ran circles around the Sony ones.

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.

Here is my explanation.

Assume there is a smoothly varying analog waveform with values at uniform time spacing, as follows. (Actually there are an infinite number of in-between points).

..0.. 1.. 2.. 3.. 4.. 5.. 6.. 7.. 8.. 9.. 10. 11. 12 etc.

If the waveform is sampled at a frequency 1/4 that of uniform time spacing of the example, (44.1 KHz perhaps) the data will look like the following:

..0............... 4.............. 8...............12..
THIS IS ALL THERE IS ON THE DISC.

A D/A reading this data, at however high a frequency, will output an analog "staircase" voltage as follows:

..000000000000000004444444444444444488888888888888812

But suppose we read the digital data just four times faster than it is really changing, add the four values up,
and divide by 4.

First point……..(0+0+0+4)/4 = 1
Second point....(0+0+4+4)/4 = 2
Third point.....(0+4+4+4)/4 = 3
Fourth point....(4+4+4+4)/4 = 4
Fifth point.....(4+4+4+8)/4 = 5
Sixth point.....(4+4+8+8)/4 = 6
Seventh point...(4+8+8+8)/4 = 7
Eighth point....(8+8+8+8)/4 = 8
....And so on

Again we have a staircase that only approximates the instantaneous analog voltage gererated by the microphone when the music was recorded and digitized, but the steps of this staircase are much smaller than the staircase obtained when the digital data stream from the disc is only processed at the same rate that it was digitized at. The smaller steps mean that the staircase stays closer to the original analog continuously ramping signal.

Note also that we are now quantized at 1, instead of 4, which is the quantization of the raw data stream obtained from the disc. A factor of 4. That’s like 2 bits of additional resolution. That’s how Phillips got 16 bit performance from a 14 bit D/A.