[JaZZ]

Quote:

Originally posted by theaudiohobby ...This amplitude value will change, if the sampling frequency changes.

I'm not sure if I get you right this time. Is this what you're trying to say? In a case where the sampling rate e.g. changes by only a few numbers, and your reference point is let's say the start of a short tone burst, then after the same defined number of samples the given waveform will cause the concerned sample to be positioned on a different place within the wave, e.g. on the edge instead on top, with as a consequence a different amplitude value. So of course you're right. Nevertheless, Joe's example with its 192/48 kHz alternatives doesn't really lead to this scenario, so I'm not sure if it's this what you mean.

Quote:

The values you keep quoting are simply the total number permutations of the n-bit word e.g. a 16-bit word has 65536 possible permutations and a 24-bit word has 16,777,216 permutations. And these permutations correspond to the smallest to the largest value of the given n-bit word, which I think is what you are referring to as steps.

I'm not happy with your wording. A step is the minimum possible amplitude-value change from my perspective -- insofar your wording isn't clear. With PCM, at every moment you have the whole bandwidth of the given bitrate at your disposal, but of course the incoming signal shape dictates what value is recorded by the ADC at a defined moment. Now in the case of PCM you have a very fine grid, be it 16 or 24 bit -- at least compared to the coarse 7.17-bit/141-step grid with DSD -- when it comes to catch the exact amplitude values for a signal meant to represent a 20-kHz tone.

 

[Joe Bloggs]

Quote:

Originally posted by theaudiohobby I will change tact a here a bit, how does change from frequency to an audio waveform grab you.

It grabs me very differently. But then again, that's because they are different things altogether. It looks to me like you're trying to weasel out of a big mistake by changing your statement into something correct, pretend you haven't changed anything and confuse everyone in the process.

edit: changed smiley

 

[theaudiohobby]

Quote:

Originally posted by JaZZ I'm not sure if I get you right this time. Is this what you're trying to say? In a case where the sampling rate e.g. changes by only a few numbers, and your reference point is let's say the start of a short tone burst, then after the same defined number of samples the given waveform will cause the concerned sample to be positioned on a different place within the wave, e.g. on the edge instead on top, with as a consequence a different amplitude value. So of course you're right. Nevertheless, Joe's example with its 192/48 kHz alternatives doesn't really lead to this scenario, so I'm not sure if it's this what you mean.

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.

Quote:

I'm not happy with your wording. A step is the minimum possible amplitude-value change from my perspective -- insofar your wording isn't clear. With PCM, at every moment you have the whole bandwidth of the given bitrate at your disposal, but of course the incoming signal shape dictates what value is recorded by the ADC at a defined moment. Now in the case of PCM you have a very fine grid, be it 16 or 24 bit -- at least compared to the coarse 7.17-bit/141-step grid with DSD -- when it comes to catch the exact amplitude values for a signal meant to represent a 20-kHz tone.

The relationship that you seek to establish by means of dividing the sampling frequency by the frequency of the signal to be encoded does not work all it does is establish the number of sample points at that frequency. And all those sample points record are relative amplitude differences between each adjacent sample point it is reasonable to assume that the number of sample points required will be less at higher frequencies. The dynamic range begins fall off when the number of sample points become increasing less than optimal. However that is obviously not the case @20KHz which is the reason you still have better than 120dB at this point.

 

[JaZZ]

Quote:

Originally posted by theaudiohobby ...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.

Why should they? Either you accept the above scenario or the answer is no.
Quote:

The relationship that you seek to establish by means of dividing the sampling frequency by the frequency of the signal to be encoded does not work...

I have dificulties to read your message because there are some punctuation marks missing... However: Mathematically it works very well...
Quote:

...all it does is establish the number of sample points at that frequency. And all those sample points record are relative amplitude differences between each adjacent sample point...

(...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.
Quote:

...it is reasonable to assume that the number of sample points required will be less at higher frequencies.

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 which 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.
Quote:

The dynamic range begins fall off when the number of sample points become increasing less than optimal. However that is obviously not the case @20KHz which is the reason you still have better than 120dB at this point.

Here I can't follow you at all.

Believe me, I have not the least interest to see SACD as a bad format, and so far my sonic experience with it indicates that it's really not bad at all. But I can't swallow the theoretical disadvantages, and after all I feel challenged to fight unreflected adulation.

 

[theaudiohobby]

EDIT

 

[Joe Bloggs]

theaudiohobby,
Quote:

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.

In my example that you quoted, the SAME numbers

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...

And if the bit depth is 16 bits, it represents a FULL SCALE pure tone, whether it's 16 bits at 44.1kHz, 48kHz, 96kHz, 192kHz or whatever (yes you can have 16/96 and 16/192, there's no rule saying that the bit depth must increase as the sample rate increases...)

...that make any sense to you?

 

[theaudiohobby]

Jazz,

In response to your last post
Quote:

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.

Quote:

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

Quote:

(...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
Quote:

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

Quote:

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.

 

[Joe Bloggs]

Quote:

And from what I read it is actually a vector value that also stores the relative frequency difference

theaudiohobby, in DSD as well as PCM the frequency of the signal is *never* explicitly encoded in the individual samples, the frequency (or frequencies) contained in an audio signal can only be calculated by taking many adjacent samples at once for analysis. Perhaps you need to find some elementary physics textbook to read up on what a frequency is and an elementary textbook on digital signal representation to read up on how it is represented in PCM, let alone DSD

Quote:

therefore [LPCM is] stuck with absolute values.

And what is wrong with that?

Quote:

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.

And what is this supposed to mean?

Quote:

[size=xx-small] 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, And from what I read it is actually a vector value that also stores the relative frequency difference. 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. 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[/size]

 

[Joe Bloggs]

Brief explanation of 'frequency' as follows

A 'frequency' can be defined as 'the number of times something repeats in one second'. Suppose the waveforms above are being read at a rate such that we move through the distance indicated in the 'unit of time' in one second. Then the purple wave repeats itself 4 times in 1 second, and the green wave repeats itself once in 1 second. (the others do not repeat for a exact whole number of times) The purple wave has a frequency of 4 Hertz (Hz) and the green wave, 1 Hz.

PCM takes a sample of the waveform 44100 times a second. So if you take 44100 adjacent sample points from PCM and find that the same pattern of points repeats itself 4 times a second, the samples are said to encode a 4Hz frequency.

----------
Now can you see why a single point in the waveform, or a single sample in PCM, can not be said to have a 'frequency'???????

----------
Also, the number for a sample point only encodes the vertical position of the point in the waveform, this does not vary with sampling rate! Thus if the top position of the purple waveform is assigned position 65535, it will be position 65535 whether the sample rate is 44.1kHz, 48kHz, 96kHz and 192kHz!!!

I can't believe you were arguing with me about 'frequency resolution', 'noise floor at frequency x', 'impulse response', etc. when you didn't even know what a frequency is!!!!