why BW is half the signalling rate in PCM transmission ?

[desperado1]

transmission channel bandwidth for pcm

why the bandwidth is half the signalling rate in PCM transmission ?

 

[rramya]

pulse code modulation bandwith

Hi desperado1
In digital we always refer sampling rate Rs = No. of samples (sent)per sec as bandwidth.
As per nyquist theorem, sampling freq should be atleast twice the maximum content of the signal freq .

Therefore, bandwidth is half the signalling rate in PCM transmission .

Happy learning.

 

[desperado1]

theoretical maximum signaling rate

Thanks for the reply..........As far i know from your reply is that Bandwidth refers to the no of samples per second. I am still not clear about the signalling rate and its relation to that of Bandwidth. i m new to this feild. Can u please elaborate this to me.........

 

[rramya]

m-ary and nyquist formula

I am really sorry for the mislead information.

Thank you very much for pinpointing.

well back to your question.

let me rewrite your question

WHY IS SIGNAL BANDWIDTH IS HALF THE SIGNALLING RATE?
answer:
first the formula :
maximum rate of information transmission of PCM systems. (SIGNALLING RATE)
R_b =2W log2 L bits/sec

if L=2, (i.e., L==> No. of representation level of the quantizer)

Then, R_b =2W bits/sec
which obeys nyquist theorem.

note:
As per nyquist theorem, sampling freq should be atleast twice the maximum content of the signal freq

suppose if L=M^n which represents the possible code words.

then R_b =2W log2 (M^n) bits/sec

R_b =2Wn log2 (M) bits/sec

this formula applied to M-ary PCM syatem, where the parameter average power transmitted(P),noise power (No) in the particular bandwidth B
are included reduces to final eqn

R_b = B log2 ( 1+ 12P/(k^2 No B ) )

where
No B = variance of the channel noise measured in bandwidth B

This eqn can be compared with Shannon's channel cpacity theorem.
C= B log2 ( 1+ P/ No B)

Note:
here the channel capacity is the maximum signalling rate (R_b)

i am very very sorry in my previous message i have wrritten Signalling rate as bandwidth. It is wrong.

Actualy maximum signalling rate is te channel capacity in digital comm systems.


Happy learning