Why Is Audio Sampling Rate 8Kbps in TDM and How Is Frame Length Calculated?

I have been studying the concept of Time Division Multiplexing, but I have not been able to understand some stuffs, for instance, I have not been able to understand why the sampling rate for audio is 8Kbps and then they say the frame length is 128ms, I saw on another documents that the frame length would be 1/8000 which gives 128µs, I am really getting confused, as a matter of fact I am confused, on another documents I was also asked to Explain Time Division in terms of sources and their bit rates. I would like some help on all these please, maybe a little explanation of the concept would be also good, so that I can view it from another persons point of view, thanks...

I found this reference on the Internet:

http://zone.ni.com/devzone/cda/ph/p/id/270

It states that "Speech from a telephone conversation is sampled once every 125 msec". If that were true, then the sample rate would be 8 Hz -- clearly incorrect, since 8 Hz is below the range of human hearing (perhaps these are telephones for Elephants ;)

No, it should be 125 µSec (i.e. as Colin pointed out, the "mu" character for "micro").

I think you are confusing 2 different subjects here.

In time division multiplexing you are sending data - voice - whatever during a certain window of time. Lets assume that you have 10 channels of data that you want to send - this would mean that every channel would be alotted 1/10 of a second - give or take a few milli-secs to send their data. When you mention frame lenth I believe you are looking at how much time do you have to send your data. Don't confuse frame length with sampling rates.


The other subject is sampling rates. For normal voice conversion a sampling rate of 8Khz would be needed to digitize a 4 Khz audio signal. Look up NYQUIST rates. Think about audio CD's they sample at a 40 KHz rate which would give a maximum audio rate of 20KHz.

You're right, I was interchanging terms -- but, still, wouldn't that 8Khz "sampling rate" need to actually be the _Frame Rate_? If you have 10 channels of telephone audio, and if each channel was sampled 1/8KHz or every 125µS, then the audio signal for one of the channels would really have a sample rate of 1.25 mS (the Frame Rate) for a sample frequency of 800Hz (at the demux point) which by the Nyquist rule would mean a top signal frequency of 400Hz -- not really conducive to intelligible conversation.

The Frame Rate would need to be 8KHz * 10 (or 80 KHz) in order to get a sample rate of 8KHz per channel, right?

I don't think I am really following, according to Nyquist , if the signal is 4KHz for audio then the sampling rate suppose to be 8KHz or more. For 8KHz, it means a sample from each channel would be taking at 1/8000 = 125µS, so what exactly is the frame rate?
Secondly, I am starting to have a confusion about channels and sources...... what I have had in mind all the while is that channels are the PCM signals from devices like a microphone, a phone set, a television etc. But it seems some serious confusion is starting to set in for me.. Please, I wouldn't mind a small explanation on that, diagrams would be helpful too. Thanks, I am so grateful.

Correct me if I'm wrong, but for a 10 channel analog time division multiplex [TDM] system (like would have been used back in the analog telephone days) with a channel time slot of 125µS, the frame rate would be 10 * 125µS = 1.25 mS.

The sample rate is the same as the frame rate because for each frame only one channel per frame is sampled -- so, for that channel it is sampled once per frame thus the frame rate _is_ the sample rate.

Thus, the frame rate needs to be the desired Audio Sample Rate/Number of Channels. So for a telephone system with a 4000 Hz cutoff frequency the per channel sample rate should be 8000 Hz or more. So, say it's 8000 Hz, and there are 10 channels, then the frame rate would be 1/8000Hz = 125µS and the channel time slot would be 12.5 µS