how to interpret FFT output

t=0:.01:2*pi;
f=cos(t);
F=fft(f)
plot(real(F))

So, I am confused about what FFT is actually outputting. I see two frequency spikes with an amplitude of pi*100. The spikes occur at 0 and 2*pi*100. Already, I see there must be some sort of relationship between the step size of my time vector and the location of the spikes. Similarly the amplitude seems to be half of the period, so there must be some sort of relationship with that as well. Can someone explain to me these relationships and how to interpret this plot?

What I EXPECTED to see was a single spike on the x axis at 1, cooresponding with cos(1*t). (What is the x-axis on this plot anyway?) Also if we relate fft to the discrete Fourier Series, does the amplitude of the spike have any relationship with the value of A_n or B_n in the summation series?

My goal is to eventually be able to take advantage of fft to solve for a steady state response given a periodic input into a linear system, but first i need to understand exactly what i am dealing with!

Thanks.

Answer 1

[dpb]

See

doc fft

example for demonstration of PSD and frequency and discussion of Matlab fft output. Basically, the magnitude is independent of the x-axis, you have to associate the sample frequency manually.

My classic reference (showing my age) is Brigham, OA, The Fast Fourier Transform and Its Applications, Prentice-Hall.

Answer 2

[Ashawaraya Shalini]

Hi, Following link will help you understand the FFT output step by step... You need to calculate the power spectral density and plot it against frequency to interpret FFT results.

https://www.mathworks.com/help/matlab/ref/fft.html

https://www.mathworks.com/help/matlab/math/fourier-transforms.html

[Sateesh Kalidas]

The link is broken. Any hints please.

[dpb]

Updated link above plus the general section on Fourier Transforms.

Locally, just type

doc fft

at command line and follow links