Can we find a function f(t) for which int_(-oo)^(oo) f(t)e^(-j omega t)dt, converges but int_(- oo)^(-oo) f(t)e^(-st)dt, does not ?

allbleachix

allbleachix

Answered question

2022-09-04

Can we find a function f(t) for which
+ f ( t ) e j ω t d t ,
converges but
+ f ( t ) e s t d t ,
does not ?
Here, j 2 = 1, ω is a real number and s is a complex number.

Answer & Explanation

Zayden Dorsey

Zayden Dorsey

Beginner2022-09-05Added 18 answers

For instance, f ( t ) = e | t | 1 / 3 , because 0 e s t | t | 1 / 3 d t diverges for s > 0
Damon Cowan

Damon Cowan

Beginner2022-09-06Added 3 answers

f ( t ) = 1 1 + t 2 is such a function.

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