# How can I relate my amplitude from a FTT to the actual signal?

Sorry for disturb you guys, I've been playing with this the last days. I am computing signals of a wave produced with a wavemaker. Cause I have several sensors (wave gauges) I am sensing the same wave in several places along the canal.

I am cutting each signal into pieces to follow one wave each, this is cause the wave transforms itself along the canal. Due to this I am analyzing pieces of a wave as it moves, lie you can see at the next image: After this, I've been playing around with the Fourier implementation of wolfram. To know how to plot it and how it works, using this I started to play with Cos[x] and Sin[x] functions. Now I know that the period below needs to be set by me and that after that the peaks of each frequency are shown below as f= 1/A if Sin[A*X].

Whit this info I plotted 2*Sin[Pi*x] and Sin[3*Pi*x], where x is given as a list that goes from 0 to 3.2 in increments of 0.025. That gives us a sampling rate of 40 for each unit (cause .025*40 = 1).

Plotting both as a signal:

So our spectrum must show two signals, one at pi/2 and the other at (1/3)*(pi/2) on the x-axis. So far so good and the 1/pi must be larger that is the second one, the 1st one must be shorter... but their amplitudes I can not get them to be honest.

The amplitudes of the 1st one must be shorter as far as I remember, cause it measures the strength of the signal at that frequency and the amplitude of the 1st one (Sin[3*pi*x]) is larger?. Meanwhile, the peak of 2*Sin[pi*x] is shorter?. Also, their numbers don't match what my intuition tells me, I was expecting the peak of one to be 2 and the other 1, but they have 8 and 6?.

I am sorting ideas of what might be happening, maybe I am getting the peaks wrong, that would explain why the peaks are reversed. Even so, what about the strength of the signal?. I know the Fourier transform is getting the transform of every number, so is scaling? or I am applying this just wrong?.