EdGrip wrote: ↑20 Dec 2017
Thanks Selig!
It's going to take some reading and head scratching to properly internalise how a wave can always be reconstructed perfectly from comparatively few sample points, irrespective of where in the cycle they happen to fall.
Another conundrum is how frequency modulation and *some distortion of a sample produces the same sidebands and harmonics as would be produced with a higher sample rate or were performed by analogue processes (ignoring aliasing for the moment)
Understanding that might give you plenty of insight.
Always remember that PCM is just a
representation of tge sound, but not the sound itself. Also note that there is a two way
transformation between PCM and the frequency spectrum. What this means is that the frequency spectrum representation is sort-of contained within the PCM, and the PCM is-sort of contained within the frequency spectrum representation.
Typically in the digital world we perform this transformation in powers of two (known as
windows), such as 64, 128, 256, 512 and 1024.
The frequency spectrum, by the way, is represented as
sine oscillators (known as
bins) with frequencies at fixed intervals (e.g. 0hz, 10hz, 20hz, ...). If you took one oscillator, like 20hz and tried to render it as a wave at the samplerate you end up with those vertical bars that needs a curve to pass through it. If you were to render all sine oscillators and then add them together, you get back the original PCM wave.
A 64 frame window gives you 64 oscillators.
The transformation process between the two are pretty identical, and there is a way to use one transformation to perform both jobs. That might not mean much to you now, but I just want drum in the idea that a wave sort-of contains more than just a wave.
So you might be looking at these few sample points unable to discern how to draw the curve of the wave, but if you remember that the frequency spectrum is contained within that wave, it becomes appararent that you can just transform the PCM to the frequency spectrum and just sum the bins. You can now render the waveform at any samplerate, and even feed it to analogue oscillators to render it all the
continuous glory that is analogue synthesis.
As selig says above, some D/A converters use the same antialiasing filter as the A/D converter, but there are other D/A methods, such as 1-bit DAC.
There are other properties of waves and signal processing that explain why your speaker can reproduce multiple frequencies just as well it could reproduce each individual frequency (except when it starts to distort, then they come with harmonics that can result in some cancellation).
*: Need to double check whether this applies to all distortion processes.
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Note to self: videos and pictures would probably help.