Estimate the bandwidth required to transmit 1Mbits/s of data using a modulation scheme which comprises 32 different frequencies and 2 amplitude levels
Yes, this is a homework question that ive been trying to do. What i have so far is the following:
I think 32 frequencies implies that i have 32 symbols, and therefore i have 64 bits, i saw somewhere that the number of bits is always 2*(number of symbols).
bps = 1Mbps = baud*bpb from here
=>baud = 1Mbps/64 = 15625
and i also saw somewhere that Band Width = 2*baud = 31250Hz
Is this correct?
-Thanks.
Best Answer
There are two roads: one that lets you understand what's happening, and another that is fast. Let's start with the firts.
please note: I'm assuming 1Mbitps = \$2^{20}\$bps and not \$10^6\$bps.
Your transmitter would divide the bitrate across 32 modulators: each modulator would see a reduced bitrate, i.e. 1Mbps/32 = 32768bps = 32kbps. Since you have two amplitude levels the baud rate and the bit rate correspond: each of your modulators works with a 32kbaud rate needing 65.536kHz of bandwidth (of noiseless channel, Shannon would add). Your total bandwidth is then your number of channels times each channel's bandwidth, i.e. 64kHz*32 = 2.1MHz (approx.).
Now for the fast way: you have a bit rate of 1Mbps, all your modulator's symbols are the same, i.e. 1 bit per symbol, so you can just double your bit rate and get the bandwidth:
2*1Mbps = 2*1.048M = 2.1MHz