On Sunday, January 9, 2011 6:52:09 PM UTC-5, Tim Wescott wrote:
...

> You're not using any frequency limiting -- are you sure you're not just
> amplifying the heck out of your noise?
>
> In Scilab:
>
> -->N = 4096; n = 0:N-1;
>
> -->nn = pmodulo(n + N/2, N) - N/2;
>
> -->x = exp(-nn.^2 / 100000); xd = ifft(fft(x) .* (-nn .^ 2));
>
> -->clf; plot2d(n, [x' xd'])
>
> gives me what looks like a very clean double derivative of the input
> Gaussian.

I suppose the double differentiation simply negates the signal, avoiding the need for phase shifts.
Jerry