On 05/07/2011 11:48 AM, Invisible wrote:
> Suppose you have 1,000 numbers chosen at random with a uniform
> distribution [-1, +1]. Now suppose you take the discrete Fourier
> transform of this sequence of numbers. Since the input is random, the
> output is also random. But what distribution does it follow?
>
> I've searched all over the Internet, and I can't seem to find the answer
> to this trivial question.
>
> My best guess is that the Central Limit Theorem would apply, resulting
> in both the sine and cosine coefficients being normally distributed.
> (But with what parameters?) The CLT definitely applies to independent
> /identically distributed/ random variables. I'm fuzzy about what happens
> when the variables are not identically distributed, however.

Apparently the sum of random variables is distributed as the 
/convolution/ of the distributions of each variable.

Post a reply to this message