1)computes the Power spectral density and Amplitude spectrum (P(f),F(f))
of 1d signal y(t) with sample rate Fs (Nyquist rate) which is known% apriori. The results are plotted in 3 figures which correspond to simple
PSD,logarithmic PSD (dB) and Amplitude Specturm respectively.
Ampitude(f) = \/ PSD(f)
2)The usefulness of this function is the adjustment of the frequency axis.
3)The fast Fourier transform is computed with Matlab built-in function
fft, but for signals whose lengths <1000 points, one can use the nested
function y=Fast_Fourier_Transform(X,N) .
figure, plot(t,y),xlabel('time (s)'),ylabel('Voltage (v)'),
title(strcat('Signal corrupted with AWGN, \sigma=',num2str(sigma))),
in the M-file Demo_FFT:
1st Part : we compute the spectrum of sinusoidal signal Y(t) with frequency Fc
2nd Part : FFT[Y²(t)]
The demo is adjusted with sample rate Fs>=4*Fc.
Youssef, if you want to obtain the power spectral density PSD (W/Hz) you should divide the power spectrum Power to equivalent noise bandwidth ENBW of the window.
S1 = sum(win);
S2 = sum(win.^2);
ENBW = Fs*S2/(S1^2);
PSD = Power/ENBW;
In your case there is no window (or there is rectangular one), so ENBW = Fs/L.
I consider it a 'power spectral' plot rather than a 'power spectral density' plot. you simply make 'power=mag^2' but it's not so-called 'PSD'.
Zhivomirov Thank you for your remark, the submission has been updated .
Figure 2 (Power Spectral Density, logarithmic scale) is not correct. The Y scale does not represent the PSD magnitude in dB. It is just the same PSD like Figure 1, but represented on logarithmic Y scale. If you want to have a PSD in dB, use PowerdB = 10*log10(Power) and plot(f, PowerdB).
errata : figure 2 is changed from semilogy(Frequency, Power) to 10*log10(Frequency, 10*log10(Power)) in Decibel .