I have calculated a sine wave of magnitude .4, rounded it, added uniform dither, rounded that, and added tpd, and rounded THAT, i.e. I've set a step size of '1' in the quantizer.
The routine that does this will follow in a comment.
The photo I'm attaching now has 4 lines. each line shows a signal. The four columns are
(signal) (signal spectrum) (error signal) and (error spectrum)
The four lines are
undithered unquantized
undithered quantized - NOTE THE SIGNAL IS GONE. POOF, LOST, MISSING, GONE. Information is ***LOST***
uniform dithered quantized - Note, signal is back, but noise level changes with data value, so data modulates noise level.
TPD - Note, signal is back at same level, noise is 3dB higher, but there is no modulation of the noise level.
This shows, clearly, visibly, and without debate, that DITHERING PRESERVES INFORMATION.
That is all!
The routine that does this will follow in a comment.
The photo I'm attaching now has 4 lines. each line shows a signal. The four columns are
(signal) (signal spectrum) (error signal) and (error spectrum)
The four lines are
undithered unquantized
undithered quantized - NOTE THE SIGNAL IS GONE. POOF, LOST, MISSING, GONE. Information is ***LOST***
uniform dithered quantized - Note, signal is back, but noise level changes with data value, so data modulates noise level.
TPD - Note, signal is back at same level, noise is 3dB higher, but there is no modulation of the noise level.
This shows, clearly, visibly, and without debate, that DITHERING PRESERVES INFORMATION.
That is all!