Signal-to-Noise-Ratio?

Question

I was wondering if any1 can elucidate how to calculate the Siganal to Noise Ratio. For example, what would be the signal-to-noise ratio needed to put a T1 carrier on a 50 kHz line?Any help appreciated

Answer 1

Dr. House is correct. Here's why, if you are working with the bandwidth of a channel and a signal to noise ratio, then you use Shannon's equation. This equation is that the maximum bits/second = the bandwidth of the channel, times the base 2 logarithm of the S/N ratio plus 1.

max bps = B log2(S/N+1)

Example, say we have a 3 KHz channel and a signal to noise ratio of 31dB. So 1+31=32 and log2(32)=5 and 5x3KHz gives a max of about 15Kbps. In your case, you'd be looking at the log base 2 of 4,294,967,296 which = 32 and 32x50,000=1.6Mbps which would fit a T1 at 1.544Mbps.

So while in theory you would need a signal to noise ratio of over 4 billion, in our universe you will NEVER achieve this, unless you find a way to get around the laws of physics! Most good signal to noise ratios (depending on the type of system) range from 10 to 100dB. A S/N ratio of 4 Billion dB is a signal with the strength of an exploding star in outer space...

Answer 2

You couldnt put a t1 carrier on a 50 khz line to begin with! The frequency is lower than the carrier would need in the first place! 50 khz is lower than the AM broadcast band and isnt much good for anything more than hi frequency audio. You are trying to put 1000 pounds of info in a 2 ounce bag!