# How to perform FFT analysis for a sinusoidal wave.

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Jith C on 5 Jun 2019
Answered: Chirag Nighut on 10 Jun 2019
Hi,
I have recorded flame. Due to buoyancy effect flame fluctuates by time. I have plotted the flame height vs time graph (Its looks like sinusoidal wave). Now how to convert this graph into amplitude (Y) vs frequency (X_Hz) graph by using FFT Matlab code. John D'Errico on 5 Jun 2019
You might start by reading the help for fft.

Chirag Nighut on 10 Jun 2019
Considering that X is the array of the flame heights at different time values and L is the number of samples of the data,
Fx = fft(X);
should give you the Discrete Fourier transform of X (Y)
Since the calculated FFT will be symmetric such that the magnitude of only the first half points are unique (and the rest are symmetrically redundant), the main idea is to display only half of the FFT spectrum. Remember that multiplying by 2 is necessary as you are adding the magnitude in the negative and positive frequency domain. The following code illustrates this point:
P = abs(Fx/L);
Y = P(1:L/2+1);
Y(2:end-1) = 2*Y(2:end-1);
Now we can plot the graph of Y ie. amplitude of the Fourier Transform w.r.t to the frequency X_Hz. Note that Fs is the sampling frequency that you decide.
X_Hz = Fs*(0:(L/2))/L;
plot(X_Hz, Y)
title('Single-Sided Amplitude Spectrum of X(t)')
xlabel('f (X_Hz)')
ylabel('|Y(f)|')

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