someone has done it for me.....
I was loading some sample sine waves into matlab to create a few plots to show what cd "quality" sampiling does to 2 waveforms. I came across this link:
http://www.skreddypedals.com/digital_sucks/index.htm
Where they have done an approxamation of the waveforms for me and written a nice analysis.
Of course that is with sine waves or near sine waves and not at all like real music. I play the flute and organ and I have been able to produce triangular waves on my flute. On the organ the flute pipes are basically sine waves and the real organ sound diapasions are more like sine waves put through a leaky diode. The various other ranks have their own distinctive sounds and can become quite complex in a rank of reeds.
As is pointed out in this link, real world music does not look even close to sine waves.
This is all very basic ( the digitizing of 2 sine waves and the resulting artifacts upon recreation of audio). What is interesting is that if you take that recreated waveform and redigitize it at a high sample rate and do an FFT on it to convert from the time to frequency domains you will see that the 2 fundamential frequencies will be frequency modulated in proportion to the quanitization error and the jitter rate. Plus you will be seeing a number of other artifacts. They show up as brief bursts of sounds that are not related to the fundamentials.
We compound this further by realizing that the above discription is per channel. The left channel has its own frequency modulation of the fundamentials. The right has its own as well. This frequency modulation is typically not perceived as a frequency change and it does average out to 0 delta compaired to the fundamential. Think of the doppler shift of a train. The pitch is higher as it comes at you and lower as it goes away but when you sum coming and going it equals the standing still pitch. (we use this in astronomy as well for rotating stars...)
However, when you compair the left to right signals you will see that the frequency modulation of each is in effect a phase shift. When the pitch is modulated higher is forms a positive phase shift reaching your ears sooner and when modulated lower forms a negative phase shift.
The phase shift per channel is random and produces 5 results:
no modulation in either channel ---------------- "normal" sound
positive modulation on left --------------------- sound shifts left
positive modulation on right -------------------- sound shifts right
positive modulation on both -------------------- sound shifts closer
negative modulation on both ------------------- sound shifts away
In thinking about the artifacts that digital playback generates it would be important to remember that a basic premis of the Fourier Series is that any specific waveform can be represented by the superposition of harmonically related sine and cosine waves. It has been suggested by a number of researchers that the brain is effect doing FFTs on the the sounds that it hears. This is one way to explain how it is possable for some people to hear (detect sounds better to me here) pitches above their upper hearing limit.
So when digital playback presents to your ears the various artifacts your brain needs to (so think some researchers) create a fourier series that approxamates the waveform. This series includes components well above human hearing. The artifacts present a significant number of series components that are transient, random and not coincident (left ear to right ear).
It is not really clear what is happening. It is suspected that the brain being a pattern matching, predictive type of machine has problems when things are not as it expects in processing these anomolies.
Now this is all very interesting and nice but it is of course just speculation of what is going on inside your head. It does tend to explain some of the observations of human hearing.
And all this from just 2 tones.
If you have hung in there and followed this then I'm impressed. I don't write code to detect submarines anymore and I was never good at implementing FFT and other DSP routines. That is what libraries are for.
The end result is that digital has a way to go yet and that cd "quality" will never be more than lo-fi. That some day digital will be able to overcome its limitations (32 bits, 512 kHz?). And I will still like to drive my 1975 Fiat Spider and spool up some tape.
Sorry about being so brief
