Why reconstruction filters? Just intermodulation distortion?

[MRC01]

OK, but to generate 32.1 kHz instead of 12 kHz, you'd need to either suppress (filter) the fundamental so only the image is present, or up sample using a scheme that also suppresses the fundamental. Both are do-able, using W-S or one of many other schemes, but AFAIK that is not what a conventional (delta-sigma or not) audio DAC would implement. ...

I think I'm lost, sorry... The theory is sound, but I do not see it happening in an audio DAC. That is, images will be present if not filtered, but the baseband signals will still be there.

Agreed that is what would happen and the way most DACs actually work. My point is that from a theoretical perspective, regardless of how DACs actually work, the set of sampling points - the audio data - has an infinite number of different solutions, many of which don't even have the original passband frequencies that were encoded to create them. Bandwidth filtering is theoretically necessary in order to reconstruct the wave that was encoded, because there are an infinite number of entirely different waves that all pass though those exact same sampling points. Even if a real-world DAC would never actually construct any of those other waves, they are all valid solutions and it is only bandwidth filtering that narrows the set of possible solutions to just a single wave.

You are not lost at all. My point has all along been from the perspective of theory.

 

[DonH56]

Agreed that is what would happen and the way most DACs actually work. My point is that from a theoretical perspective, regardless of how DACs actually work, the set of sampling points - the audio data - has an infinite number of different solutions, many of which don't even have the original passband frequencies that were encoded to create them. Bandwidth filtering is theoretically necessary in order to reconstruct the wave that was encoded, because there are an infinite number of entirely different waves that all pass though those exact same sampling points. Even if a real-world DAC would never actually construct any of those other waves, they are all valid solutions and it is only bandwidth filtering that narrows the set of possible solutions to just a single wave.

You are not lost at all. My point has all along been from the perspective of theory.

Got it, thanks.

As for this: "Even if a real-world DAC would never actually construct any of those other waves, they are all valid solutions and it is only bandwidth filtering that narrows the set of possible solutions to just a single wave." And this: "My point has all along been from the perspective of theory."

I think think you already know this, but to close the loop for myself and perhaps others: RF DACs often use the images as you say, with techniques to suppress the baseband signal and other images, to produce high-frequency signals without the need for external (analog) mixers or upconverters. Thus you are correct and it has been realized in practice. I have in the past designed such bandpass DACs both conventional and delta-sigma. My confusion was in thinking you were saying that could happen for an audio DAC, which is only possible (IME) using those techniques not normally applied to audio (or baseband in general) DACs.

We're good!