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Re: For an even greater change of pace, let's try to answer the question

I mentioned this down below but no one responded - so now that we have a fresh new round in this thread I thought I'd put some ideas forward here and get some comments.

Quantization distortion is more than just harmonic distortion - it limits the possible phases of a frequency you can represent. For the mentioned example of a 1Khz sine wave, the sampling rate is irrelavent to accurately represent it as long as that rate more than 2Khz.

The sampling theorem requires perfect filters and non-quantized (continuous) samples to give us back exactly what we put in. If we want to represent the same 1Khz sine wave at ANY phase we need non-quantized samples. Quantization limits the phases we can represent to a finite set. I haven't done the math, but inuitively (eep!) it seems this phase set is larger for the full scale 1Khz signal vs low level 1Khz signal. This distortion is not harmonic distortion - it is an inability to represent the original 1Khz signal at an arbitrary phase. The sample rate becomes a factor now _because_ of the sample level quantization. A 2.5 Khz sample rate has significatly fewer phases that can be represented than a 44.1 Khz sample rate for that same 1Khz signal given the same quantization level.

All of this focus is on the representation of a single time domain signal in which case the phase of our 1Khz sine wave is irrelavent since we do not care about the phase of a single sine wave (hence the above mentioned paper not addressing this issue). Making it a complex signal would make this distortion more important since in the frequency domain, the complex signal is a sum of many sine waves at different frequencies and phases and the relative phases of the frequency components are essential to representing the actual signal - bit depth directly influences the this distortion and dither doesn't address it.

Even with the simple 1Khz signal, 2 or more channels complicate matters. What happens to our perception of the location of the 1Khz tone if we adjust the phase of one of the 2 channels gradually? In this case the phase is equivalent to a time delay. With a digital representation of the signal we cannot gradually adjust the delay, we can only do it in steps (because the sample playback of both channels is synchronized), and the louder signals have more steps than quieter ones. This is for the simple case - so what happens with a complex signal? And what does this mean for soundstaging capability? To play back exactly the same complex signal from digital samples in two channels with an arbitrary delay requires inifinite phase resolution, so what happens with discrete phase resolution that varies with frequency and level?

Any thoughts? Any ideas how DSD and PCM compare in this regard?



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