# Comparison of data transfer between different bandwidths

Which of the following can transfer more data [bps]

1. 10Hz bandwidth over 2s

2. 20Hz bandwidth over 1s

It looks like its the same bps but I'm not sure.

In information theory, Shannon's theorem states that the channel capacity is the bandwidth in Hz, multiplied by a two-based logarithm of 1 plus the channel's signal-to-noise ratio. And that the unit of channel capacity is bits per second. Thus if you double the bandwidth, you double the bits per second. But the same amount of information flows when you send twice as long with the original bitrate. So according to Shannon's theorem, the two cases would be the same.

That said, I don't know what your instructor has been teaching and whether Shannon's theorem is the only one that applies. Maybe there's some another theory that has something to do with the amount of messages you can send in a unit of time and the effect of number of messages to the channel capacity (very important in Ethernet, for example).

• Based on the information given you are correct. I imagine that the point of the exercise (assuming this is schoolwork) is for the person to understand that the unit of Hz is 1/sec, and that time-bandwidth product is the same. – Jotorious Dec 16 '14 at 22:35
• @Jotorious, That could very well be the case. And yes, it's schoolwork - the original question stated that this was a question in a test. – PkP Dec 16 '14 at 22:36
• Doubling the bandwidth does not always double the capacity according to Shannon formula as the AWGN noise also increases with increasing bandwidth. So you need to be sure how the ratio P/(B*No) is changing before making a comment on the capacity. – Yasir Ahmed Feb 22 '18 at 17:59