Upsampling. Truth vs Marketing

The connect-the-dots metaphor is really unfortunate, because a lot of audiophiles buy into the idea that that's what a DAC does. But reconstructing an analog wave is nothing like connecting dots. More dots DOES make it easier to DRAW a wave. But as long as you have enough samples for the bandwidth, a DAC can reconstruct that wave without more information.

(BTW, the example given above didn't have enough information to do so, because it called for only two samples per cycle. You need fractionally more than two to reconstruct the wave properly.)

Imagine that, instead of a wave, you were trying to trace a straight line. The more dots you had, the easier it would be to do this freehand. But a graphing calculator would only need two points.

Pabelson...According to Nyquist, just two (error free) samples per cycle will perfectly recover a sine wave. But, in this error-prone nonsinusoidal world, where I played with digital data stream representations of analog waveforms (non audio), experience taught me that four samples per cycle was worth the trouble. That's why the 96 KHz PCM of DVDA (or 192KHz for stereo) solves the bigest problem with redbook CDs. 24 Bits is nice too.

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
>

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.