>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




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