How to compute the fourier transform for a signal u(t) over frequency band [-10,10]?

I have a signal u(t) already defined, but I need to compute the fft and plot the magnitude and phase of the fourier transform. HOW DO I DO THIS?

I TRIED FFT(U,[-10,10]), BUT DOESN'T WORK.

Answer 1

[Dr. Seis]

Say you have the following:

N = 1024; % Number of samples
dt = 0.01;  % Seconds per sample
u_time = randn(1,N);

Then, you would have:

Nyquist = 1/(2*dt);
df = 1 / (N*dt);
f = -Nyquist : df : Nyquist-df;
U_freq = fftshift(fft(u_time));

And you can plot this data between -10 and 10 Hertz by:

figure;
plot(f , abs(U_freq)*dt, 'b-'); hold on;
plot(f , angle(U_freq),'r-'); hold off;
xlim([-10 10]);
legend('magnitude','phase');

However, the above formulation assumes that your data are even. I would go further and try to pad your time data with zeros to next power of 2 (i.e., above is 2^10). Let me know if you have questions about doing that.

Answer 2

[Walter Roberson]

freqs = fft(U);
plot(real(freqs),'b*-');
hold on
plot(imag(freqs),'r+:');

[MINAS104]

what about the [-10,10] frequency band?

[Walter Roberson]

What do negative frequencies mean?

[MINAS104]

from -10Hz to 10Hz.

Could you also do this?

plot(angle(fft(u)) %phase

plot(abs(fft(u)) %magnitude

[Walter Roberson]

So -10 Hz is a signal that goes backwards in time??

Answer 3

[Honglei Chen]

Depending on your sampling rate and the number of points in your signal, you may want to also explore the following function

doc goertzel
doc czt