[theaudiohobby]

 

[theaudiohobby]

Quote:

Principles of Sigma-Delta Modulation for Analog-to-Digital Converters Sangil Park, Ph. D., Strategic Applications, Digital Signal Processor Operation ...Sometimes, the S-D modulator is referred to as an interpolative coder. The quantization noise characteristic (noise performance) of such a coder is frequency dependent in contrast to delta modulation. ... this noise-shaping property is well suited to signal processing applications such as digital audio and communication. Like delta modulators, the S-D modulators use a simple coarse quantizer (comparator). However, unlike delta modulators, these systems encode the integral of the signal itself and thus their performance is insensitive to the rate of change of the signal.

 

[theaudiohobby]

Quote:

Originally posted by JaZZ As far as I'm concerned, the corresponding resolution values for 20 kHz and the different formats are as follows: CD..............16 bit DVD(-A).......24 bit (up to) SACD...........7.17 bit (equivalent) 2,822,400 : 20,000 = 141.12 = 2^7.17 [corrected: 241.12 --> 141.12] [/B]

Correct me, if I am wrong, LPCM is a series of absolute n-bit words with the largest n-bit word being at the Nyquist cutoff frequency and the smallest n-bit word at DC (that is 0Hz) for a given sampling frequency. Therefore in LPCM, the size of a given n-bit word is proportional to the sample point position wrt to the sample frequency. In other words, these are absolute values and the issue of steps as you potray it does not really come into play at all. And the bit-depth is contant over the entire bandwidth in line with this principle.

On the hand, DSD being SDM is a series of adjacent n-bit words with each successive n-bit word encoding the relative amplitude difference between successive adjacent sample points. Therefore in this case, each sample point corresponds to a single bit, so you have 141 'adjacent' bits to capture a signal at 20KHz. Your calculations do not seem to take into account that these are 'adjacent' 1-bit words as opposed to a single absolute n-bit word of 141 as your text seems to wrongly presume.

 

[xtreme4099]

its a never ending battle it seems ...

 

[JaZZ]

Quote:

Originally posted by theaudiohobby Correct me, if I am wrong, LPCM is a series of absolute n-bit words with the largest n-bit word being at the Nyquist cutoff frequency and the smallest n-bit word at DC (that is 0Hz) for a given sampling frequency.

Frequency is not encoded in the samples, just amplitude values. So each sample has the same word length: 24 bit. The «largest» word in terms of value is the one which indicates maximum amplitude. Frequency is the result of the shape of the curve resulting from the sample values.

Quote:

Therefore in LPCM, the size of a given n-bit word is proportional to the sample point position wrt to the sample frequency. In other words, these are absolute values and the issue of steps as you portray it does not really come into play at all. And the bit-depth is constant over the entire bandwidth in line with this principle.

Yes, the bit-depth is constant with (L)PCM. (Why «L» in this context? Is there any nonlinear PCM in play we have to exclude?) But I don't understand the reference to the sample frequency. And the steps are a digital-inherent phenomenon anyway. In graphics you have a bit depth of 8 bit per color channel (at 24 bit), that means you have 256 brightness values (= steps) at your disposal. Correspondingly in high-rez PCM with its 24-bit word length you have 16,777,216 amplitude values/steps at your disposal.

Quote:

On the hand, DSD being SDM is a series of adjacent n-bit words with each successive n-bit word encoding the relative amplitude difference between successive adjacent sample points. Therefore in this case, each sample point corresponds to a single bit, so you have 141 'adjacent' bits to capture a signal at 20KHz. Your calculations do not seem to take into account that these are 'adjacent' 1-bit words as opposed to a single absolute n-bit word as your text seems to assume. In other words, summing the bits in the manner that you have done does not really work.

In fact DSD doesn't use word lengths expressed in bit, there are no such codes, but you can calculate the equivalent to a PCM bit depth -- for comparability purposes --, that's why I've always used the term «equivalent» in the context of DSD's dynamic resolution. In turn you could simply compare the number of amplitude values/steps available for each format at a certain frequency -- this shows the relations even better. For 20 kHz it's 16,777,216 for DVD and 141 for SACD (whereby -- of course -- in the case of PCM this number doesn't ever change with frequency).

 

[theaudiohobby]

Quote:

Originally posted by JaZZ Frequency is not encoded in the samples, just amplitude values. So each sample has the same word length: 24 bit. The «largest» word in terms of value is the one which indicates maximum amplitude. Frequency is the result of the shape of the curve resulting from the sample values.

Yes, However the same word represents a different amplitude at different sample rates. except of course, if this is what you are actually trying to say.

PS: the amplitude is a function of the frequency of the signal wrt to time.

Quote:

Yes, the bit-depth is constant with (L)PCM. (Why «L» in this context? Is there any nonlinear PCM in play we have to exclude?) But I don't understand the reference to the sample frequency. And the steps are a digital-inherent phenomenon anyway. In graphics you have a bit depth of 8 bit per color channel (at 24 bit), that means you have 256 brightness values (= steps) at your disposal. Correspondingly in high-rez PCM with its 24-bit word length you have 16,777,216 amplitude values/steps at your disposal.

Actually, you do not have 16,777,216 amplitude values/steps at your disposal in that sense, Your amplitude can only be one of these possible of values at a given sample point. A different amplitude value (n-bit word) at the sample point will give you a totally different signal not a different volume/power output perse.

Quote:

In fact DSD doesn't use word lengths expressed in bit, there are no such codes [/B]

You have lost me here completely, what are you trying to say here exactly when you say DSD doesn't use word lengths expressed in bit, there are no such codes, 141 is the number of sample points and on an SACD, each of those sample points will have a 1-bit word and that is a binary word with a wordlength of 1. As mentioned previously In LPCM @192KHz, a 20KHz signal will have only nine sample points and only a maximum of nine of the possible 16,777,216? values (n-bit words) will be valid amplitude values for this signal with only one amplitude value/step being valid at each respective sample point.


PS: LPCM - Linear Pulse Code Modulation
DPCM : Differential Pulse Code Modulation, of which Sigma Delta Modulation is a DPCM process.

EDITED: For clarity

 

[Joe Bloggs]

/me falls off chair laughing

 

[JaZZ]

Quote:

Originally posted by theaudiohobby Yes, However the same word represents a different amplitude at different sample rates.

Hey, no! Why should it?

Quote:

...the amplitude is a function of the frequency of the signal wrt to time.

No. The amplitude is the amplitude.

Quote:

Actually, you do not have 16,777,216 amplitude values/steps at your disposal...

For one single sample you have the choice between 16,777,216 amplitude values, but of course you have to decide for one value.

What's your point actually?
Quote:

...what are you trying to say here exactly when you say "DSD doesn't use word lengths expressed in bit..."

If you like, you can name one bit a «word» (I know in English there are quite a few words consisting of only one letter

)). I was trying to make clear that there is a fundamental difference with encoding between PCM and DSD, but that the calculations as to dynamic resolution are nevertheless compatible.
Quote:

As mentioned previously in LPCM @192KHz, a 20KHz signal will have only nine sample points and only a maximum of nine of the possible 16,777,216? values (n-bit words) will be valid amplitude values for this signal with only one amplitude value/step being valid at each respective sample point.

Correct. But what's the pont?

You have a quite good command of the digital terminology and know how to use some keywords, but the longer the discussion lasts, the more I get the impression that you don't really get the idea of how digital works. Your digital world appears to be quite obscure and complicated. I've tried to convey you some ideas in a naive manner to enable you a more intuitive access (because that's what you need!), but you have refused to take them seriously -- probably because of the lack of «professional» terminology. Sorry, no offense meant, but that's my impression.

 

[theaudiohobby]

First I think you should try reading the thread more carefully, the point you are trying to make is not valid at all. And Joe Bloggs made the point very impressively a few posts back.

Quote:

originally posted by Joe Bloggs Oh yes there is. 0 65535 0 -65535 0... This is a pure tone at 48kHz! *for 192kHz sample rate. It could also be a 12kHz tone for 48kHz sample rate, etc.

Need I say more!

There is no need to continue at this point rather I leave you to critique this document. Lastly forget the naive language (or is it layman terms) and stick to the correct terms, it easier to follow your posts that way.

EDIT: changed the link

 

[JaZZ]

Quote:

0 65535 0 -65535 0... This is a pure tone at 48kHz! *for 192kHz sample rate.

the audiohobby...

...again, I really don't know what your point is. Joe is absolutely right here. This is a pure tone (sine wave) of 48 kHz in the case of a sampling rate of 192 kHz. It may at the same time be a triangle wave, but resolution at 1/4 of the sampling rate is still not enough to differentiate.

At this moment you've lost a secret admirer of your «professional» attitude...

 

[theaudiohobby]

Sigh...what are you saying exactly?

The speed of your reply will suggest that you have not consulted the the lecture notes. oh well...

 

[JaZZ]

First let me ask about the intention behind the quotation of Joe's example.

Maybe my reply makes more sense to you then.

 

[theaudiohobby]

Quote:

Originally posted by JaZZ First let me ask about the intention behind the quotation of Joe's example.

This discussion is really going nowhere but for the sake of politeness, I will continue, in LPCM a fixed n-bit word corresponds to a different amplitude for different sampling frequencies i.e. the n-bit word will correspond to a different amplitude for each change in sampling frequency. In your posts, you repeatedly, though wrongly state that the choice of the n-bit word is somewhat arbitary which is clearly wrong. The relationship between the n-bit words and their actual values is fixed wrt the analog signal being encoded. The encoding process just a'int gonna fly otherwise.

PS: And you really should drop the peace sign because you being rude whilst not straying the posting rules. and I HATE THAT!!!!!

 

[JaZZ]

Quote:

Originally posted by theaudiohobby ...in LPCM a fixed n-bit word corresponds to a different amplitude for different sampling frequencies i.e. the n-bit word will correspond to a different amplitude for each change in sampling frequency.

Look, that's a great error of yours! (And not the only one.) Amplitude has nothing to do with frequency. It can't be, because a single sample still doesn't define a «frequency» -- it's just an amplitude value, catched by a microphone during a hundredth of a millisecond --, only together with the neighbored samples it can form a frequency. But it can just as well form a sort of noise with undefined dominating frequency. What does your theory foresee for such a case? You see, it doesn't make sense. And the values stay the same independent of sampling rate, just a different bit depth changes the things.

Sorry for appearing rude, it wasn't my intention! But I also have noticed that your own tone hasn't always been the finest.

 

[theaudiohobby]

I will change tact a here a bit, how does change from frequency to an audio waveform grab you. And the amplitude is simply capturing the height of the incoming waveform with a fixed time relationship which is the clock of the sampling frequency. Therefore the actual value of the n-bit words and their adjacent relationships is fixed wrt the audio waveform. Each permutation of an n-bit word will corresponding to exactly to 1 amplitude value. This amplitude value will change, if the sampling frequency changes. Each n-bit word corresponds to a single sample point, and there are only 9 sample points @ 192 KHz for a 20KHz pure tone signal and each n-bit word has a predefined value that I cannot be bothered to calculate but it sure is not arbitary. The values you keep quoting are simply the total number of 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 actual n-bit values from the smallest to the largest value, which I think is what you are referring to as steps.