From Sampling Theorem we know that if be a band-limited signal with

, then is uniquely determined by its samples

if

,

where

Now,

(a)

Here, obviously, .

Hence can be recovered exactly from .

 

(b)

Here, obviously ,

Hence can be recovered exactly from .

 

(c)

Real part of , but we can't say anything particular about imaginary part of the , thus not necessary that for this particular range.

Hence cannot be recovered exactly from .

 

(d) real and

As is real we have

Taking mod on both sides

So, we get

Here , obviously ,

Hence x(t) can be recovered exactly from .

 

(e) real and

Proceeding as above we get

Here, obviously ,

Hence x(t) cannot be recovered exactly from .

 

(f)

When we convolve two functions with domain to and to then the domain of their convolution function varies from to .

Here, and

Therefore,

Here, obviously ,

Hence x(t) can be recovered exactly from .

 

(g)

We cannot say anything about ,

Hence x(t) cannot be recovered exactly from .