I'm currently going over some past papers to prepare for an exam. I'm looking at the problem I've attached in the image. I know how to do (ii) and (iii) but I can't get my head around (i)? Surely the absolute bandwidth is infinite given the range of the sum but we've been constantly told that we can't have infinite bandwidth so I'm a bit confused?

 

A square wave theoretically has an infinite amount of harmonics, each having a frequency that is a pair(as far as i remember) integer multiple of the fundamental.
So it goes like this for 1Khz square: 1KHz, full amplitude;2Khz, half amplitude;4KHz, a quarter of the amplitude; 6KHz, a eight of the amplitude, up to infinity.
We can't have infinite bandwidth response in real circuits because of their frequency-dependant reactive features.
That's quite a load of data and i have no clue on fourier.
In the end, the answer is up to you.Check the context of your exam to choose the right answer.

 

Hi,

Actually a square wave has fundamental amplitude 4/pi, and there are only odd harmonics like 3,5,7,9, etc., with amplitudes (4/pi)/3, (4/pi)/5, (4/pi)/7, etc., but it does to infinity at least in theory. There might be something else in the course work material that would tell us what they really want to know.