What would be the conditions on $f(x)$ such that it's Fourier transform $F(k)$ would be monotonically decreasing from $k=0$ to half range ($F(0)$ would be the maximum, and it would "fall" on both sides).

For example, it is true if $f(x)=q^x$, for any $0<q<1$. This is also true for a Gaussian function.

What would be the general conditions for this to hold?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.