This question is strange enough so I'm beginning to suspect a typo/misinterpretation.

Let be defined by

Show that is admissible and compute its normalization constant.

First of all it is very strange to think of the fourier transform to be a function on the reals as opposed to a sequence, right? (I suspect this might be a typo)

Anyway, I interpret admissible to mean: satisfies the Orthonormal Conjugate Quadrature Filter Conditions.

So first I actually find by taking the inverse fourier transform:

and this is zero at all integer values, which makes it a very strange trivial case (which is not orthonormal).

Any thoughts?

Thanks.