Using fft with rectangularPulse

I have created the following script to plot a rectangular pulse, the magnitude of the Fourier transform and the phase of the transform.

% Plot Fourier Transform

f=@(t) rectangularPulse(-1,1,t);

time=-6:0.01:6;

pulse=f(time);

fourier=fft(pulse);

figure()

subplot(3,1,1)
plot(time,pulse)                % Pulse

subplot(3,1,2)
plot(time,real(fourier));       % Magnitude of Fourier

subplot(3,1,3)
plot(time,imag(fourier));       % Phase of Fourier

I know that the Fourier transform of a rectangular pulse is a sinc function but the output I get is not.

Answer 1

[Star Strider]

It is now:

f=@(t) rectangularPulse(-1,1,t);
time=-6:0.01:6;
Fs = 1/0.01;
Fn = Fs/2;
Freq = linspace(-Fn, Fn, numel(time));
pulse=f(time);
fourier=fft(pulse);
figure()
subplot(3,1,1)
plot(time,pulse)                                % Pulse
subplot(3,1,2)
plot(Freq,fftshift(real(fourier)));             % Magnitude of Fourier
xlim([-10 10])                                  % (Optional)
subplot(3,1,3)
plot(Freq,fftshift(unwrap(angle(fourier))));    % Phase of Fourier
xlim([-10 10])                                  % (Optional)

Use fftshift to centre the amplitude and phase plots.

I also calculated the frequency vector for the ‘fourier’ plots.

Answer 2

[Samra Shazadi]

a = 0.3;

t=[-2:0.01:2];

x = rectpuls(t, a); %rectangle waves

subplot(2,1,1); %subplot for rectangle waves

plot(t,x);

axis([-1 2 0 2]);

title("Rectangle waves");

xlabel('time');

ylabel('Value');

X=fft(x);

subplot(2, 1, 2); %subplot for Frequency signal

plot(t, fftshift(abs(X)));

title("Frequency Signal");

xlabel('freq (Hz)');

ylabel('|Y(freq)|');