# Thread: Interesting Question...

1. ## Interesting Question...

I have a question here that reads as follows:

Suppose that g(t) is such that the Fourier Transform g'(s) is zero outside [a,b]. Show that g(t) is determined uniquely by its values at a sequence of points spaced 1 / (b-a) units apart.

Any help is greatly appreciated!

2. ## Additional details

If additional details are needed, please let me know!

3. Originally Posted by Majialin
I have a question here that reads as follows:

Suppose that g(t) is such that the Fourier Transform g'(s) is zero outside [a,b]. Show that g(t) is determined uniquely by its values at a sequence of points spaced 1 / (b-a) units apart.

Any help is greatly appreciated!
Okay, just to clarify:

$g'(s) = \int_{-\infty}^{\infty}g(t)e^{-ist}dt
$

and

$g'(s) = 0$ for $s < a, s >b$
$g'(s) \not\equiv 0$ elsewhere

Is this the transform you're describing?

4. ## Clarification

The notation for g'(s) should actually be g(s) with a "^" above the g. I think that is the right transform though...