OT, again, re voice bit rates and sampling rates
Dave, thank you for making the distinction between bandwidth and throughput rate.
The term bandwidth is one of the most abused and maligned in our industry (second, perhaps, only to broadband when referring to dsl and cable modem residential rates) and I have written about this until I was blue in the face in the past. I eventually saw no further gains in fighting the tide, however, and alas, I, too, have begun using the term incorrectly. But 'bandwidth' literally has to do with a band, or a 'range,' of analog frequencies, and the term 'throughput' has to do with digital bit rates. Usable throughput rates? Well, that's another discussion.
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I haven't any arguments with the rationale or the approach you used in calculating equivalent bit rates in the digital realm for frequencies in the voice range. The "times two" sampling rate formula is correct.
Here's where I have some difficulties, though. If you want to cite actual T1 channel throughput derivatives (such as your citing 56k as a T1 channel in your message) and actual sampling rates in the same paragraph, then you should stick to one set of rules and assumptions, and that should be, since you have cited T1, the rules that are actually used by T1 systems.
T1 systems assume that each of their 24 channels will pass a minimum of ~ 4 KHz, not 3 KHz. The 3 KHz bogie is a holdover benchmark from older forms of analog carriers like N carrier and L carrier which used FDM. Even some of these used 4KHz channel slots, but the upper ranges of them were reserved for signaling on hook and off hook conditions, and a certain portion at the very highest of the band was used for guardband purposes, between channels. Truth be told, these actually occupied the range between ~300 Hz and 3700 Hz, inclusive.
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True, most tariffed offerings will not guarantee frequencies greater than 3100 Hz. But that doesn't mean that they don't pass them, since the telcos have always been notorious for telling you what your worst case conditions will be, but not your best case.
And this is why they use a sample rate of 8,000 samples per second (for 4 KHz bandpass) and not 6000 samples per second for 3 KHz, as you erroneously cited.
Also, the T1 channel rate is 64 kb/s inclusive of all of the overhead bits you mentioned, and then some, and not 56 k. It is only identified as a 56 k channel after the eighth bit in the digital octet (effectievly 8 kb/s, since that bit, too, is being sampled 8000 times per second) has already been removed from the line signal by the carrier's and the customer's channel service units, reducing the usable line rate from 64 kb/s to 56 kb/s.
Again, I agree with your technique for deriving equivalent digital throughput quantities from their analog origins, but I disagree with the actual figures you used for the actual types of channels you cited.
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Regarding high fidelity over T1 carrier sampled facilities:
In earlier times, carriers and program service providers would take multiple 64 k channels (up to three, four or five of them, depending on the grade of service desired) and, when combined, this would have the effect of increasing the sample rates to as much as 40,000 samples per second: 5 * 8000 samples/sec = 40,000 samples/sec.
Using your "times two forumla, then, you can see how 20 KHz high fidelity audio was achievable over T1 facilities. For stereo, two sets of these were used, and so forth. This is still the way many systems operate today, but these are giving way to upgraded means using compression, especially for spot events, such as concerts, sporting events, etc.
More recently, ISDN codecs have been employed which use MPEG Layer 2 and 3 algorithms. These effectively do the same thing with only one or two 64 kb/s slices of bandwidth. There I go again with that word... I meant throughput.
The above paragraphs dealt with dedicated circuit technologies and ISDN. With improvements in DSP techs, however, lower throughput rates will be required, and these will be able to achieve comparable levels of fidelity, not only on dedicated and ISDN switched facilities, but on IP routed ones, as well. Thanks for hanging in ther with me.
Regards, Frank Coluccio |
