The problem of autocorrelation function

According to a differential equation in matlab, the time series x(t) is obtained. To obtain the autocorrelation result of the following figure, xs(t)=x(t-s), s is also a variable, how to write a program in matlab.

Answer 1

[Image Analyst]

Isn't it just

autoCorrelation = xcorr(x, x);

but that seems so obvious so I'm wondering if this is your homework problem and you have to not use the MATLAB function and write your own version of it. If so, read the following link:

How do I get help on homework questions on MATLAB Answers? - MATLAB Answers - MATLAB Central

If it's not homework, xcorr() should work for you.

[wenxin liu]

Thank you,it's not my homework.It is a question when I read the article.However, what I cannot understand is. I use t∈(0,5e-5) to solve the differential equation to obtain the time series x(t). At the same time, s∈(0,5e-5), x(t-s) has two variables. I can’t do anything about it

[wenxin liu]

And, I used xcorr(a,b) at the beginning, but the relationship between the variable s and t made the result of the second time delay sequence x(ts) not normally obtained. After that, I used the Fourier transform: ifft (fft(x(t)*exp(-i*2pi*s/t))), but both s and t change. I don't know how to do it. what should I do?

[Image Analyst]

What differential equation? Your first sentence of your original post about differential equation has nothing to do with the rest of the post about correlation. You don't even show any differential equation, just an equation for correlation.

And how did you define your (badly-named) "a" and "b"?

What is the time difference between two samples?

[wenxin liu]

Sorry, please forgive my mistake.

Here are my steps:

Step 1: I solve the differential equations (1,2) through ode45(), and get E(t),N(t)

Step 2: Let x(t)=E(t); then perform equation 3.xcorr(x(t),x(t-s)).

But s is also a variable with scope, it belongs to (0,5e-9). So I don't know what to do.

[wenxin liu]