# How to calculate transmission capacity?

My textbook doesn't explain how they got the answer to this question:

"If a transmission channel uses an analog carrier wave that is modulated by eight amplitudes and sixteen frequencies per bit time, then what is the transmission capacity of that channel in bits per bit time?"

I don't understand how they got the answer and I can't find any good sources online to explain it.

• I've edited my question; please take a look to see if it's useful. – MBaz May 3 '16 at 14:11

The question as stated doesn't make sense. In particular, "sixteen frequencies per bit time" doesn't mean anything. So, I'll try to guess at what the question actually is, and try to point you in the right direction.

Let's break the question in two parts. First, we're told that the carrier can have eight different amplitudes. This means we can encode three bits in the carrier amplitude. If we label amplitudes $L_0,\ldots,L_7$, we can encode the bit sequence $000$ as amplitude $L_0$, $001$ as amplitude $L_1$, etc. This means that this carrier can transmit bits 3 times faster than a carrier with only two allowed amplitudes.

The second part of the question seems to indicate that you actually have sixteen carriers, all operating simultaneously. (and that they don't interfere with each other). Each carrier can have eight different amplitudes.

If you take $R$ as the baseline rate obtained by a single carrier with two amplitudes, you should now be able to calculate the rate of 16 carriers with 8 amplitudes each, as a multiple of $R$.

Edit: I think there is a second possible interpretation of the question: this could be some sort of combination ASK-FSK, where there are 16 possible frequencies (FSK) and each could have 8 possible amplitudes (ASK). Each frequency would carry 4 bits and each amplitude a further 3 bits, for a total of seven bits per symbol time.

• So does that mean that the bits per bit time would be 7 because 2^3 and 2^4? – Isabel May 1 '16 at 19:17
• Not quite.. if one carrier transmits 3 bits, and you have 16 carriers, how many bits in total can you transmit? – MBaz May 1 '16 at 19:49
• 48 bits per bit time, that makes sense. – Isabel May 1 '16 at 20:08
• If you found the answer helpful, please don't forget to accept and/or upvote :) – MBaz May 1 '16 at 20:11