# I Understanding Fourier Transforms

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1. Oct 25, 2016

### MxwllsPersuasns

Hello all,

First time poster here so please excuse any mistakes as I'm unfamiliar with the conventions of this forum. Also before I get started I'd like to say I wasn't sure exactly where a question like this would go; I debated in the Math Programs and Latex section but figured general physics would find it the most exposure.

So I am currently working in a lab as an undergraduate assistant and much of my work involves/will involve analyzing the Fourier transforms of various electrical signals. To do this I am utilizing LabView; so our signal comes in and is displayed on a waveform graph then runs through the 'FFT' tool in LabView and the output (the transform) is displayed on a second graph with a numerical indicator array to view the particular values. My goal currently is to understand and be able to interpret a Fourier transformed waveform -- or as my professor put it "Determine, quantitatively, how to go from analog voltage to the Fourier Spectrum plotted by LabView".

Given this; I have some background knowledge I'd like to lay out to help contextualize my issue and also some specific questions I'm hoping someone can help me tackle from another angle or shed some light on;

So I know that (in essence) a Fourier Transform decomposes a time varying signal in the time domain to it's constituent trigonometric functions in the frequency domain. I was playing around with a 1V, 102Hz signal being generated from a function generator today by varying the sample rate and the number of samples (essentially varying the sampling time) and noticed that there was an inversely proportional relationship between the sampling time and the width of the 102Hz signal peak, so that, for example, if I halved the sampling time from 1s to .5s I notice that my width increases to 150%, the progression down to fractional integer times (1/n; 1/2, 1/3, 1/4, etc...) did not seem to be linear however. I was wondering if anyone might be able to shine a bit more light on this relationship or at least point me in the right direction?

Finally I have a very limited understanding of whats going on inside the software to compute the transformed values, I believe it goes something like this; First, each value in the array for the input voltage gets put through the transformation formula which produces a complex # for each value then, I believe, the complex numbers get absolute valued then squared in order to produce a real-valued number and that is what is plotted as the amplitude against the frequency. So thus if the value of the input voltage is in units of Volts then the value of the amplitudes would be in units of Volts^2. Can anyone tell me if this is correct? On the right path? Or am I completely off-base? Any insight or help into these two main issues (especially the latter -- about how the values are computed algorithmically) would be incredibly valued and appreciated. Thanks guys!

2. Oct 25, 2016