How is the decay of a signal exemplified in a Fourier Transform?

Is there any way to tell if a signal is decaying from its fourier transform?

• Is it possible to post a plot with a view of your signal? – A_A Apr 8 '19 at 4:36
• I don't have a specific signal. I'm interested in any insight into what phenomena decay (monotonous) introduces into the fourier transform – Artemmm Apr 8 '19 at 6:20
• Be more specific give a mathematical formula for your problem then we can help you otherwise I have to flag it as unclear of what you are asking. – Ch.Siva Ram Kishore Apr 8 '19 at 11:19
• I edited to be more specific – Artemmm Apr 8 '19 at 18:19
• All signals that have finite energy and thus have Fourier transforms in the classical sense (no impulses a.k.a. Dirac deltas anywhere) must decay away to $0$ as $t \to \infty$ or $\to -\infty$. So a dead giveaway is "no impulses in Fourier transform? signal decays" – Dilip Sarwate Apr 10 '19 at 4:12