fft showing frequency components at double rates

Hi there

worked with Lumerical (photonic simulating software) i got a output Time domain-signal and wanted to see it's spectrum via fft , so i used fft but the plot is showing me components at double rate which lumerical moniter visualizing spectrum shows the right spectrum, so i wondered why it is, if you have an experince or such it would be great , and Here's my code for making this happen:

clear all

close all;


%  rng('default')
%  fs = 100;                                % sample frequency (Hz)
%  t = 0:1/fs:10-1/fs;                      % 10 second span time vector
%  y = (1.3)*sin(2*pi*15*t) ...             % 15 Hz component
%   + (1.7)*sin(2*pi*40*(t-2)) ...          % 40 Hz component
%   + 2.5*randn(size(t));                   % Gaussian noise;
%  
%  figure(1)
%  plot(t,y)

load TE0_time_signal.mat;

t=lum.x0;
y=lum.y0;

figure(1)
plot(t,y)
grid on
xlabel('Time in s')
ylabel('Output field Magnitude')

time_step=t(2);



fft_y = fft(y);
% 
 fs=1/time_step;
 
 
%  [A,B,C,D] = butter(20,[192.668e+12 192.945e+12]/fs);
% d = designfilt('bandpassiir','FilterOrder',20, ...
%     'HalfPowerFrequency1',192.668e+12,'HalfPowerFrequency2',192.945e+12, ...
%     'SampleRate',fs);

n = length(y);              % number of samples
f = (0:n-1)*(fs/n);         % frequency range
power = abs(fft_y).^2/n;    % power of the DFT

figure(2)
plot(f,power)
xlabel('Frequency')
ylabel('Power')

% 
y0 = fftshift(fft_y);       % shift y values
f0 = (-n/2:n/2-1)*(fs/n);   % 0-centered frequency range
power0 = abs(y0).^2/n;      % 0-centered power

figure(3)
plot(f0,power0)
xlabel('Frequency')
ylabel('Power')

as you can see plot worked and showed the frequency components for my output time-signal

at the top of script (comment lines) i added a sinus function to test this script and it works well and shows right components, i got this script from mathworks platform,

My script should show frequncy components at 192.806 THz , 193.431THz ,194.055 THz but shows these at 385.612 THz, 386.862 THz , 388.11 THz (around 0.3e+15 in plot)

can somebody tell me why is that? And How it can be solved right to get right plot?

i have a guess which may be relevent that Nyquist theorm for complex signals states that the fsampling is maximum frequency that you can show unambigiously which in real signals are fsampling/2

Thanks

Answer 1

[David Goodmanson]

Hi Sina,

Here is an observation and a possible answer. If you expand out plot(t,y) (I used

xlim([4 4.1]*1e-12)    )

there are about 4 cycles in 10^-14 sec, or 400 THz, I think the fft is working correctly, given what its input is. However, you say you are fft-ing the magnitude of the signal. To me y doesn't look exactly like the magnitude of a signal might, but it is certainly always positive.

If you do an fft on a signal cos(2*pi*f0*t) you of course get peaks at +-f0. But abs(cos(2*pi*f0*t)) has twice as many oscillations per unit time as does cos(2*pi*f0*t). So you get peaks at 2*f0, plus a bunch of other smaller peaks that don't really seem to be showing up.

[Sina]

Thank you very much,

because of your response i found the answer, it was because i had taken magnitude of the signal in lumerical, which had to turn the option into Ey in monitor , IMO it was because of calculating magnitude that it made it look like it has double the frequency thats why it was showing exact things in double frequency it had to show, so i corrected it and it showed it correct and it was because of your answer thank you very much

Best luck in your works

Sina