I'm facing with a simple probability problem.
I have a even symmetry function p[k],
p[k] = 0 if |k| > K. p[k] can be any finite even symmetry function.
And I have the same length of random noise n[k].
n[k] follows normal distribution with a variance .
Now I want to find a distribution of following;
where . After MATLAB simulation, I realize that follows a normal distribution. But I cannot derive it.
Would you please give me a hint to solve this problem?
Thanks in advance.