# Conditions for finite bandwidth

I'd like to know which conditions must be satisfied in order to get a signal with a finite bandwidth.

• In order to get a signal with a finite bandwidth, the bandwidth of the signal must be limited so that it is not infinite. Is that what you want to know ? – AlexTP Sep 1 '17 at 8:28
• in the time domain – Gennaro Arguzzi Sep 1 '17 at 9:10
• Finite support in one domain (frequency) requires infinite support in the other (time). – hotpaw2 Sep 1 '17 at 17:37
• No. Necessary, but not sufficient. – hotpaw2 Sep 2 '17 at 5:48
• Any Gaussian distribution/function? – hotpaw2 Sep 2 '17 at 7:04

According to the Paley-Wiener theorem, functions with compact frequency support (corresponding to Bernstein spaces) can be extended from the real line to the complex plane $\mathbb{C}$ as entire functions of exponential type; entire functions are holomorphic at all finite points of $\mathbb{C}$ , exponential type means that $|f(z)|\le C e^{a|z|}$. They can be called $B$-functions.