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I would be grateful for some direction on this.

I wish to implement the following -

Given a deterministic signal (the feedback signal of a closed-loop stable system) I would like to plot the power spectral density.

The definition I am working with is this:

Implementation (MATLAB):

% Given a signal the plot of the power spectral density over the frequency range 0.1-5 rad/s is given by

% The continuous time fourier transform

w=.1:.1:5; % 0.1 to 5 rad/s (frequency range of interest)

% Compute the transform

for ii=1:50 % For each frequency increment (50 samples over the interval 0.1:0.1:5)

yy1=um.*sin(w(ii)*t) % where t is a vector of dimension [1, 3610] and um is the time series in question

yy2=um.*cos(w(ii)*t) %

% the intergral

yi1=trapz(t,yy1);

yi2=trapz(t,yy2);

% square of the fourier transform i.e. |X(omega)|^2

trans(ii)=(yi1^2+yi2^2);

end

figure(1)

plot(w, trans) % |X(omega)|^2

% For a deterministic signal no need to compute the expected value, the power of the signal is instead given by

% Energy: integral of the square of the Fourier transform wrt to frequency

energy = trapz(w, trans);

figure(2)

plot(w,energy) % sadly things have gone awry HERE!

% Power

power = energy / t(end); % where t(end) is the duration of the signal in question

figure(3)

plot(w, power)

The PSD should be a real valued nonnegative function of omega not a constant. Any prompts would be much appreciated!

I wish to implement the following -

Given a deterministic signal (the feedback signal of a closed-loop stable system) I would like to plot the power spectral density.

The definition I am working with is this:

Implementation (MATLAB):

% Given a signal the plot of the power spectral density over the frequency range 0.1-5 rad/s is given by

% The continuous time fourier transform

w=.1:.1:5; % 0.1 to 5 rad/s (frequency range of interest)

% Compute the transform

for ii=1:50 % For each frequency increment (50 samples over the interval 0.1:0.1:5)

yy1=um.*sin(w(ii)*t) % where t is a vector of dimension [1, 3610] and um is the time series in question

yy2=um.*cos(w(ii)*t) %

% the intergral

yi1=trapz(t,yy1);

yi2=trapz(t,yy2);

% square of the fourier transform i.e. |X(omega)|^2

trans(ii)=(yi1^2+yi2^2);

end

figure(1)

plot(w, trans) % |X(omega)|^2

% For a deterministic signal no need to compute the expected value, the power of the signal is instead given by

% Energy: integral of the square of the Fourier transform wrt to frequency

energy = trapz(w, trans);

figure(2)

plot(w,energy) % sadly things have gone awry HERE!

% Power

power = energy / t(end); % where t(end) is the duration of the signal in question

figure(3)

plot(w, power)

The PSD should be a real valued nonnegative function of omega not a constant. Any prompts would be much appreciated!