How to integrate Pwelch with Matlab

[windsea]

Dears,

Please help hem in order to resolve this problem.

I estimated an power spectral density using welch method with Matlab program (Pxx).

Now, I want apply this integration

m[n] := Integral from f=0.0001 to f=0.001 over S(f) * f ^ n . In my case I think that m[n] := Integral from f=0.0001 to f=0.001 over Pxx(f) * f ^ n !

After several tests I did not succeed to make this integration.

Please help me in view to intruduce this application within my code:

load wave.dat
x=wave(:,1);
fs=0.011;
u = length(x);
[Pxx,f] = pwelch(x,800,400,u,fs)
pwelch(x,800,400,u,fs)
f=0.00001 :0.0000.1/100 :0.0001 ;n=0
Z=trapz(f,Pxx)*f^n

I send also the continuous equation in the attached file
Thank you in advance

Windsea

 

[NateD]

Answer: The code you provided assumes that Pxx is a vector, whereas Pxx is actually a matrix since it was created by pwelch. You need to index each element of Pxx as Pxx(i) when calculating the integral. Therefore, you would need to use a loop to iterate through each element of Pxx and calculate the integral for each one using the trapz function. Here is an example of what the code would look like:load wave.datx=wave(:,1);fs=0.011;u = length(x);[Pxx,f] = pwelch(x,800,400,u,fs)pwelch(x,800,400,u,fs)f=0.00001 :0.0000.1/100 :0.0001 ;n=0Z = zeros(length(Pxx),1);for i = 1:length(Pxx) Z(i) = trapz(f,Pxx(i))*f^n; endThe vector Z will contain the result of the integration.