Matlab: Fourier transform of Rectangular pulse has VERY HIGH zero frequency compoent

Question

I am trying to get 1D Fourier transform of Rectangular pulse. Everything else appears fine; the zero frequency components appears very high and seems like a discrete peak.

Plot of FFT (link to jpeg image): https://drive.google.com/file/d/0B0Ah9soYnrlIYmw0UTJRNGhrWFE/edit?usp=sharing

I would appreciate if someone can tell me what am I doing wrong.

My Matlab code:

function FFT_1D_Example()

    Tau = 10e-3;    %CEST duration in second    
    NoOfPtsOnPulse = 1000;
    %Time scale for the pulse
    t_Pulse = (0:1:NoOfPtsOnPulse-1)*(Tau/(NoOfPtsOnPulse-1));      % in sec   
    B1Max = 1;          % in tesla; current value = 3 uT 

    %% Simulating the pulse shape      
    %Reactangular pulse
    B1_Array_Rect       = ones(1, length(t_Pulse))*B1Max;
    B1_Array_Rect(1)    = 0.0;
    B1_Array_Rect(end)  = 0.0;
    y = B1_Array_Rect;

    figure(1);  plot(t_Pulse, y);  title('Pulse shape');  xlabel('time (seconds)')

    %% FFT
    [Y, NFFT] = Return_1D_FFT(y);
    % Shift zero-frequency component to center of spectrum
    Y = fftshift(Y)

    % Plot single-sided amplitude spectrum.
    figure(2);  plot(abs(Y)) 
    title('Two-Sided Amplitude Spectrum of y(t)')

end
function [Y, NFFT] = Return_1D_FFT(y)
    L = length(y);
    NFFT = 2^nextpow2(L); % Next power of 2 from length of y
    Y = fft(y,NFFT);
end

glglgl glglgl · Accepted Answer · 2014-03-20T13:37:48

What kind of rectangular impulse is that? -1 to 1 or 0 to 1? I suppose it is the latter.

In this case, by merely looking at your pulse, you see it has an average value above 0. This reflects a so-called DC component, which is the 0 value of your FFT.

Matlab: Fourier transform of Rectangular pulse has VERY HIGH zero frequency compoent

1 Answers