Autocorrelation Method

Questions
, ,
1

I would like to use the autocorrelation method and I need to use the Fourier Transform defintion. The problem is that I can’t define the (w). Mathematica takes long time to run the code and finally say : A very large output was generated . the following is the code:

g1[\[Theta]_] := Sscar[rff, \[Theta], \[Pi]/2]/norm ;
h1[\[Theta]_, w_] := Sscar[rff, (\[Theta] + w), \[Pi]/2]/norm ;
data = Table[ Integrate [ g1[\[Theta]]* h1[\[Theta], w], {\[Theta], \[Theta]z, \[Theta]\[Pi]}], {w, 0.5, 1.5, 0.1}]
ListPlot[data]
2

Hi. There isn’t enough code here to see what is going on. What is the definition of Sscar for instance? Additionally, for what purpose would you like to use autocorrelation? When you say you can’t define the variable “w” what do you mean?

3

Dear ,
The Sscar is define as the Intensity of a sphere using Mie Theory .
So (w ) is the shifted when we used the Fourier Transform as : Inetgral { Sscar (theta) * Sscar (theta +w)}
and I need to use the autocorrelation method to see how is the Intensity changes with theta .

4

I’m not familiar with this area, and so not sure what (w) is in this case. If you are having issues programming something in Mathematica, perhaps you can describe what you would like to do mathematically. It looks like your evaluating this autocorrelation: Integrate[Sscar (theta) * Sscar (theta +w),{theta, -Infinity, Infinity}]

Does that integral evaluate for you? If not, maybe a symbolic integral isn’t obtainable and you may want to use NIntegrate to get a numeric approximation. Does it work for specific values of w?

5

Dear ,
I will try and see
Thanks in advance