Where is the problem? I couldnt find it.

I'm investigating into wave statistics derived from records in time and frequency domain. I used the Bretschneider Spectrum Formula in order to create linear waves. I created 400 linear waves and I sumed of them. In that case irregular wave was created. I defined the exact time domain (1258 s). After I used the Fourier Transform for getting spectral density. I think my results are enough for now. But mine spectra and Bretschneider spectra dont fix. Where is the problem? I cant understand. Please, I need help !!!

 clc,clear,close all
 %PARAMETERS%
 t1=1258;   %Exact Time Domain
 wn=400;    %Wave Number , components
 SS=8;      %Sea State

 %STRUCTURE%

 for i=1:400
     Q=2*pi.*(rand(1,wn));    %Phase
 end

 t=transpose([0:0.1:t1]);
 w1=2/wn;  
 w=[0.005:w1:2];
 if SS==8       %Sea State 8 
 Tm=16.4;       %Modal Period
 Hs=11.5;       %Significant Wave Height
 scale=0.275;   %Scale
end
if SS==6        %Sea State 6
 Tm=12.4;       %Modal Period
 Hs=5;          %Significant Wave Height
 scale=0.1;     %Scale
end
if SS==4        %Sea State 4
 Tm=8.8;        %Modal Period
 Hs=1.9;        %Significant Wave Height
 scale=0.0321;  %Scale
end
 Wm=2*pi/Tm;    %Modal Frequency

 %Bretschneider Spectrum%
 S=(5.*(Wm.^4))./(16.*(w.^5)).*(Hs.^2).*exp((-5.*(Wm.^4))./(4.*(w.^4)));

 a=transpose(sqrt(S.*2*w1)); %Amplitude
 d=sin(t*w+Q)*a;             %irregular wave
 grid
 plot(t,d)

 %FOURIER%
 spk=fft(d);                  %fourier transform%
 spkg=abs(spk);               %magnitude of fft%
 figure; plot(fftshift(spkg))
 figure; plot(2*fftshift(spkg)/t1)
 fr=[-50:100/(t1*10):50];     %sizing%
 X=(fr/2+0.1);                    %frequency%
 Y=(2*fftshift(spkg)/t1);     %spectral density%
 grid
 plot(X,Y)
 xlim([0,2]);

 %SMOOTHING%
 windowSize = 21; % Decrease for less smoothing, increase for more smoothing.
 Y = conv(Y*scale, ones(windowSize, 1), 'same');

 figure;
 grid
 plot(X,Y)
 title('Smoothed Y', 'FontSize', 20);
 xlim([0, 2]);
 drawnow

 %CHECK THE RESULT%
 wk=[0.01:0.01:2];
 S1=(5.*(Wm.^4))./(16.*(wk.^5)).*(Hs.^2).*exp((-5.*(Wm.^4))./(4.*(wk.^4)));
 grid
 plot(X,Y,wk,S1)
 xlim([0, 2]);

 %Calculating Areas%
 hold on
 Mine_Spectrum=trapz(X,Y)
 Brts_Spectrum=trapz(wk,S1)
 hold off

[KALYAN ACHARJYA]

Any code error?

[Gurkan Yilmaz]

there arent any code error.

[KALYAN ACHARJYA]

Answer 1

[KALYAN ACHARJYA]

In line, 32 t and w have different length, for multiplication both vector length should be same, the same case for 'a' too. For multiplication, vector dimension should be same.

[Gurkan Yilmaz]

Actually my problem is that Bretschneider Spectrum and mine spectrum are not same and also their graphs areas are different :( if you start the system, you can see the results easily and you can understand my problem maybe.

[KALYAN ACHARJYA]

your code having an error, how you got the results.

[Gurkan Yilmaz]

I copied my sharing and I started again, There is no error :D