how to estimate integral scale of turbulence, Lu, from Ru(τ) by numerical integration.

my question is how to estimate integral scale of turbulence, Lu, from Ru(τ) by numerical integration from time lag interval 0 to 10 secs only. My code is

 load('wind_data_part1.mat')
Fs=25; % sampling frequency of the signal, samples/second
TO=1/4; % maximum period, 1/Hz
N=7495;
U_N=V.*cosd(phi);
U_E=V.*sind(phi);
U_t=((U_N).^2+(U_E).^2).^0.5;
U_m=sum(U_t)/N % problem 1.a) mean wind direction

 u_t=U_t-U_m;
figure
plot(time,u_t) % problem 1.a) zero-mean turbulence component
xlabel('Time (sec)')
ylabel('Zero-mean turbulence, (u_t)')
legend('Zero-mean turbulence, u_t vs. time t')

 Dt=1/Fs;
R_tau=xcorr(u_t);
figure
plot(R_tau) % problem 1.b) plot R_tau as a function od time lag tau
xlabel('Time lag (sec)')
ylabel('Correlation')
legend('Correlation')

Some people suggest me to use trapz function but I need the specific limit time interval for the integral of R_tau

Many thanks!

Answer 1

[John D'Errico]

So you have data sampled over some arbitrary set of points in time, and you wish to compute the integral over some time limits that need not lie at the sample points?

1. Interpolate using a spline.

2. Integrate the spline function over the desired limits.

WTP?

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