Thread: 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!

If additional details are needed, please let me know!

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:


and

for
elsewhere

Is this the transform you're describing?

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