FFT of a square pulse in MATLAB problem

[fysiikka111]

I am trying to compute the Fourier transform of a square pulse with MATLAB's FFT.
Code:

Fs=1000; %Sampling rate (Hz)
T=1/Fs; %Sampling time interval
P=10; %Period of pulse
t=0:1/Fs:P/2; %Time axis
N=length(t);
x=rectpuls(t,P); %Pulse amplitude
n=pow2(nextpow2(N)); %Number of frequency components
Y=fft(x,n);
freq=Fs/2*linspace(0,1,n/2+1);
subplot(1,2,1)
plot(t,x)
subplot(1,2,2)
plot(freq, 2/N *abs((Y(1 : n/2+1))));
xlim([0 2])

Magnitude at the first frequency component should be 10, but is giving a result of 2. Why is this occurring?
Thanks

 

[jedishrfu]

Here's what MATLAB says about the FFT function:

https://www.mathworks.com/help/matlab/ref/fft.html?searchHighlight=fft&s_tid=doc_srchtitle
and wikipedia on FFT:

https://en.wikipedia.org/wiki/Fast_Fourier_transform
One thing to look at in your algorithm is the Nyquist frequency limitation that is a common source of frustration to first time users of the FFT() function.

https://en.wikipedia.org/wiki/Nyquist_frequency

 

[whoohm]

It looks like the original question is several years old, but there is a recent reply.

Here is some Matlab code to demonstrate the FFT of a non-periodic square pulse. This will give you the correct amplitude. It will also plot the mag and phase spectrum.

ts=50;
t=-ts:.1:ts;
x=zeros(size(t));
x(450:550)=ones(1,101);
subplot(4,1,1)
plot(t,x)
axis([-ts,ts,-.1,1.1])
title('CONTINUOUS-TIME NON-PERIODIC PULSE SIGNAL x(t)  [duration 10 sec]')
xlabel('Time  t (sec)')
Tw=10;
fs=2;
f=[-fs:.005:-.005,1,.005:.005:fs];
X=(1./(pi*f)).*sin(pi*f*Tw);
X((length(f)-1)/2+1)=Tw;
f((length(f)-1)/2+1)=0;
subplot(4,1,2)
plot(f,X)
axis([-fs,fs,-3,12])
ylabel('Fourier Transform X(f)')
xlabel('Frequency f (Hz)')
subplot(4,1,3)
plot(f,abs(X))
axis([-fs,fs,-3,12])
ylabel('Magnitude Spectrum |X(f)|')
xlabel('Frequency f (Hz)')
subplot(4,1,4)
plot(f,angle(X))
axis([-fs,fs,-4,4])
ylabel('Phase Spectrum arg{X(f)} (rads)')
xlabel('Frequency f (Hz)')

 

[jedishrfu]

Yes, we were doing spring cleaning on some old threads trying to provide meaningful content so your post is welcome.