In response to your last post
|Originally posted by theaudiohobby
Closer but not close enough, the sampling frequency determines the highest frequency of the audio waveform that may be successfully encoded as per the Nyquist frequency. Therefore as the Nyquist cutoff frequency changes, the amplitude values for each respective n-bit word will change.
|Originally posted by JaZZ
Why should they? Either you accept the above scenario or the answer is no.
I have dificulties to read your message because there are some punctuation marks missing... However: Mathematically it works very well...
Did you mean Why shouldn’t they
|(...record...?) Yes -- and that's even exactly my point! Because the difference is always only one amplitude step of the available 141, whereas you would need the thousandfold to passably compete with PCM.
That's where I absolutely agree with you. I'm quite sure 24 bit is luxury for high frequencies alone. But with PCM you have to deal with low-frequency signals of high amplitudes carrying high frequencies that have smaller amplitudes by themselves but nevertheless together with the lows need the whole dynamic headroom. Here DSD behaves differently. But the discrepancy is nevertheless far too gross IMO. [Addendum:] I've realized retroactively that you wrote «sample points», not «amplitude values», as which I erroneously interpreted it -- so unintentionally I've brought a new factor in favor of DSD into play
Firstly, I was indeed speaking of sample points because each sample point will have a 1-bit word (in SACD) and each 1-bit word represents two values that is 0 and 1. In other words, two permutations per sample point. However this does not address your objection. I think you are failing to connect the fact that in DSD (or SDM as a whole) the amplitude differences are based on the preceding adjacent values
. I will not pretend to fully understand noiseshaping, but Sanjil Parks excellent, though lengthy tutorial goes into considerable detail about the Noise transfer function so it is not voodoo science, as some will suppose. However I think I understand the quantization process better, to get a delta value, the modulator is continually integrating the last output delta word to an LPCM word and then feeds it back into the input of the quantizer, then it takes the delta of incoming integral word and the integral of last output word i.e. the quantizer always integrates and feeds back the last output to the input of the modulator and then takes the delta difference between the input and the last output, from then on noiseshaping takes care of the rest. However it is clear to see that the process will break down once the noiseshaper cannot generate sufficient dynamic range because the frequency is not fast enough (analogous to insufficient sample points or 1-bit words). Therefore the fact it has sufficient dynamic range at 20KHz means that 141 sample points are sufficient. I think predictive scalar quantization
describes the process perfectly since the delta value is always based on the integral of the last output.
ADDENDUM: I got the name of the process from the quote below
|Predictive coding Derjavitch, Deloraine, and Van Mierlo
(1947), Elias (1950, 1955), Cutler (1952), DeJager (1952).
Predict next sample based on previous reconstructions, Code prediction error (residual) Predictive scalar quantization (DPCM, delta modulation, ADPCM, Sigma Delta modulation). Virtually all speech coders use some form of predictive coding
However in LPCM n-bit words are not relative but absolute, therefore you are stuck
with absolute values. Though at first glance LPCM seems more flexible, it is not because the amplitude value for each n-bit word is defined and fixed wrt to the sampling frequency. When you change sampling frequency even though the n-bit words stay the constant, the amplitude value and frequency of the n-bit word changes. or as Joe Bloggs
keeps reminding me
|0 65535 -65535 0 65535...
can be used to encode a pure tone of different frequencies depending on the sampling frequency. The numbers *don't* need to get larger as the sampling frequency increases, you just need to read more of the numbers per second...
EDITED: Edited the text.