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.
