What would be the point?
We have established that low level signals can be severely distorted by quantization, and that a nominal application of dither removes much, but not all, of that distortion.
David - What does the frequncey spectrum analysis of that 50 HZ dithered look like
pdq -look at the 2nd image in 2bdecided post68 above . On first looking the dither seems to have not removed the distortions at all.
Use the FFT to check that the harmonics are not there and the dither is doing what is expected
do the fft to confirm that the harmonics are not there. Anyone looking at the statisticle analysis would suspect that they are.
The image in post 77 is way to square. A reconstructed dithered waveform should look like a fuzzy sine wave .
which could effect the listening experience
is a genuinely original revelation in digital audio engineering
But to see that statistical analysis done on music would prove that digital audio is fundamentally constrained in amplitude variation, with a statistical variance, around the quantization levels, which could effect the listening experience, and is a genuinely original revelation in digital audio engineering.
I'm not sure why anyone thinks a filter at 22kHz is going to change a square-ish low frequency waveform that much. The example I posted was a low amplitude sine wave at 50Hz; at 8-bits it ends up with square-wave-like transitions at ~250Hz due to quantisation. In this example, you can comfortably fit the first 40 harmonics within the transition band. That's more than you need to make a square wave look something like a square wave.Cheers,David.
Because that is how it is taught in textbooks. Typically a stream of spiky samples is shown going into a reconstruction filter and out the other side comes a smooth wave. As the cooledit images shows the reconstruction filter and dither do neither. As your plot shows the output is a stream of jumps between quantization levels, which illustrates my original point in the listening test topic about a quantization grid accept rather than a grid it is more of a vertically spaced grating.
When you say 8x oversampled to simulate reconstruction can you confirm that that includes simulation the 22Khz low pass filter.
But to see that statistical analysis done on music would prove that digital audio is fundamentally constrained in amplitude variation, with a statistical variance, around the quantization levels
I am a member of the Audio Engineering Society by the way.
Between the sample points, the reconstructed signal could go anywhere - though for a given input signal there's only one "correct" place for it go (defined by the sinc function) and that may or more likely may not be on an original quantisation step.
Since you're talking about time being filled between points that are sampled you would expect the waveform to fall between quantization levels.
My text books on the subject speak clearly about quantization error, so I reject KMD's claim to the contrary. Maybe the problem has to do with glancing at pictures instead of reading the text and equations?
What about ringing?