What signaltonoise ratio is needed to put a T1 carrier on a

What signal-to-noise ratio is needed to put a T1 carrier on a 50-kHz line? Data rate on a T1 line is 1.544 Mbits/sec.

Can you please show me step by step how to do it

Answer:

We have given :

Data rate on a T1 = 1.544Mbits/sec.

Now H * log( 1 + S/N) = H * 1.544 * 10^6 , Now put H(bandwidth of the line) = 50000 , S = average signal power , N = average noise power.

=> 50000 * log ( 1 + S/N ) = 1.544 * 10^6

Now , S/N ( Signal Ratio ) = 2^30 - 1 = > 93 db