>All right, John-- > >A couple of years ago (discreet cough), Cisco gave away copies of books as >promos. One was _IP Telephony_ by Gorlaski and Kolon (McGraw Hill, 2000). >GOOD BOOK. On pp 77-78 is an explanation of the Nyquist rate and voice >sampling:
Well, if it comes from MANY years ago, before even MY time, Nyquist started publishing his work in the 1928 Bell System Technical Journal. I don't have a copy handy, but, if anyone really cares, I do have a copy somewhere of Shannon's 1948 book "The Mathematical Theory of Communications," itself an extension of a BSTJ article, that I think quotes Nyquist. *sigh* and people around here think one is ancient when one refers to a mainframe, or bisync, or analog... > >"...Thus, if an analog voice signal reaching up to 3400Hz is to be sampled >at the Nyquist rate, the sampling frequency must be at least twice that, or >6800Hz, or samples per second. > >"Sampling does not have to be done at the Nyquist rate. The Nyquist rate is >a minimal requirement to reproduce the input waveform, but sampling can be >done at rates higher or lower than the Nyquist rate. If sampling takes place >at rates lower than the Nyquist rate, the result is distortion of the >waveform known as (italics) aliasing. Aliasing just means that there is more >than one output waveform that fits the 'connect the dots' pattern of the >samples. There is no aliasing ast the Nyquist rate and above." > >They go on to point out that, by sampling at a rate above the Nyquist rate, >you have more than the minimum required information to reliably reconstruct >the voice signal at the destination. This allows you to lose a few samples >in transit (not that such things would ever happen, of course) and still >have only one possible reconstruction. Sampling at 8000Hz means there is a >4000Hz voice bandwidth (overly generous but convenient because 4 is a power >of 2 and that makes it easier to code in a binary system). > >And from the 8000 samples/sec, each of which sends 1 8-bit word, we have the >DS0 of 64000 bps (why only 56000 bps may be usable is a separate issue, >having to do with signaling on telephone links). Nyquist's model refers to PCM encoding, representing any sample in 8 bits. Even before we get into compression, there are more bandwidth-efficient, standardized encodings, such as ADPCM at 32 Kbps or less. > >Annlee >""John Neiberger"" wrote in message >[EMAIL PROTECTED]">news:[EMAIL PROTECTED]... >> This is OT, but the upper limit of human hearing is actually >> around 20KHz at best and usually drops to around 16KHz or so. >> If your upper limit starts to drop below that you'll start to >> notice that it's difficult to hear clearly. (Sorry, in my >> other life I'm a sound engineer and musician.) >> >> I've heard that the 4KHz limit is because there is a low-pass >> filter used for voice. I can't remember the exact reason, but >> that information plugged into the Nyquist theorem explains--as >> Priscilla mentions--why a DS0 is 64Kbps. >> >> Okay, time to do some serious studying once I'm through being >> lazy and drinking this coffee... >> >> John >> >> ---- On Tue, 26 Feb 2002, Priscilla Oppenheimer >> ([EMAIL PROTECTED]) wrote: >> >> > At 08:06 PM 2/26/02, Rafay wrote: >> > >How do you describe Sample Rate.? >> > >> > In what context? The term is sometimes used when describing >> the analog >> > to >> > digital process, for example when digitizing voice. Voice >> produces an >> > analog wave as your lungs and tongue press against the air. >> An analog >> > wave >> > has infinite possible values. Computers can't deal with >> infinity. They >> > work >> > with discreet numbers. The solution is to sample the analog >> voice many >> > times per second. Sampling means to take a snapshot. >> > >> > The sample rate is how often the analog wave is sampled. >> Nyquist showed >> > that you have to sample at twice the rate of the highest >> frequency that >> > may >> > occur in the original data. Most humans don't output (and >> can't hear) > > > anything about 4 KHz. So sample 8,000 times per second (8Khz) >> and the >> > result will be good enough. When using a sample rate of 8,000 >> KHz, if >> > each >> > sample is saved in an 8-bit byte, the resulting data rate is >> 64 Kbps. >> > That's one DS0. Compression allows us to use a smaller data >> rate, with >> > some >> > loss in fidelity. >> > > > > Priscilla Message Posted at: http://www.groupstudy.com/form/read.php?f=7&i=36629&t=36566 -------------------------------------------------- FAQ, list archives, and subscription info: http://www.groupstudy.com/list/cisco.html Report misconduct and Nondisclosure violations to [EMAIL PROTECTED]