# MATLAB - remove the frequency at zero in FFT

I am getting a high frequency at 0Hz. How can I remove it? I am not supposed to get it.

My code is

W = 3.64*2*pi;

Fs = 50;                      % Sampling frequency in hz
T = 1/Fs;                     % Sample time
L = 1000;                     % Length of signal
t = (0:L-1)*T;                % Time vector
v = 113*(1+0.40*sin(W*t));

theta0 = 12*(pi/180);         % in radians for 12 degree
theta1 = 6*(pi/180);          % in radians for 6 degree
theta = theta0-theta1*sin(W*t);

Lift = 0.5*1.225*v.^(2)*(2*pi).*theta;

NFFT = 2^nextpow2(L);         % Next power of 2 from length of Lift
Y = fft(Lift,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2+1);

subplot(2,1,1);
plot(Fs*t,Lift);

subplot(2,1,2)
plot(f, 2*abs(Y(1:NFFT/2+1)))
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Small hint. I suggest you to use dec2rad function for conversion to radians. – jojek May 12 '14 at 7:19

Frequency bin at zero is simply mean value of your signal. Just take a look on definition of DFT, for zero frequency $k$ we get:

$$\left. X[k]=\sum_{n=0}^{N-1}x[n]e^{-i 2\pi n\cdot k} \right |_{k=0} \Rightarrow X[0]=\sum_{n=0}^{N-1}x[n]e^{-i 2\pi n\cdot 0} = \sum_{n=0}^{N-1}x[n]$$

So after you calculate the FFT and divide by number of samples, indeed you get the mean value of your signal. In order to remove that, please apply the following before the FFT calculation:

Lift = Lift - mean(Lift);
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It worked. But I don't understand the concept of this frequency bin. Can you explain if possible? – Vinlite May 12 '14 at 6:53
@Vinlite: Please check the updated post. – jojek May 12 '14 at 6:55

## protected by jojek♦Feb 18 '15 at 22:57

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