I need to integrate the folowing integral: 1/T * integral x^2(tau) dtau [t+T/2, t-T/2]

hi, guys

I need to integrate the folowing integral:

1/T * integral x^2(tau) dtau [t+T/2, t-T/2]

tau should be chosen from user, we can choose 1 sec.

x=Discrete data, with dt=0.005

T=Short time interval.

Thank you if you help me

[Dyuman Joshi]

How does this related to MATLAB? Is it an assignment? Then show your code/what you have tried and tell what problem/error you are facing.

Also, tau is the variable of integration, how can it assume a value? Maybe format your formula properly, it is still a bit ambiguous.

Answer 1

[Walter Roberson]

syms T t tau x
result = 1/T * int(x^2 * tau, tau, t-T/2, t+T/2)

result = 

tau should be chosen from user

No, that is inconsistent with you integrating with respect to tau (the dtau in your expression) . The variable of integration cannot have a value chosen by the user.

Perhaps t is being chosen by the user?

x=Discrete data, with dt=0.005

Does that imply that x is a function of t? The same t that is being used in the bounds? If so then you should not be doing an integral, and should instead be doing a numeric summation or perhaps a trapz over the x that are in the range t-T/2 to t+T/2

[navid jafari]

hi, Thanks,

yes, tau is the variable of integration and x is a function of t.

mybe you are right, I should do a simple sum instead of an integral. For example, if I consider tau to be 1 second, I will do summation on every 200 data.

It is a transformation on the signal and finally the answer must be another signal.

How can I use the trapz function for this purpose?

[Walter Roberson]

Under the condition that T is an odd integer (not even!!)

u_i__hat = movemean(u_i.^2, T)

If T were even then the window would not be centered the right way.

[navid jafari]

Thank you again

Nothing is mentioned in the original article about T being odd or even.

we can find the temporal root-mean-square functions from the real data (according that formula) with this code.

This code will probably work.

but,In your opinion, how should we select the tau selection condition in this code?

Thanks

[Walter Roberson]

In your original, T is a time, but in this code, T is the number of points to use in the window. There could be theoretical differences if the desired window time does not happen to be a multiple of the sample rate.