Module 3 : Sampling and Reconstruction
Problem 8
 
Solution 8

(a) We know that

*is a periodic square wave of period .

 

With as shown in the figure.

 

Figure (a)

 

We calculate as follows: (FT of a periodic signal)

where,

Considering any one period , (say from 0 to ) and

Substituting 

which can never be 0.

Thus, is an impulse train situated at intervals of .

And has a maximum value of .

(Maximum value of T without aliasing).

 

 

(b) We know that

*is a periodic square wave of period .

With as shown in the figure.

 

Figure (b)

 

We calculate as follows: (FT of a periodic signal)

where

Considering any one period , (say from 0 to T) and

Substituting 

 

for (i.e. k is even )

Thus, is an impulse train situated at intervals of .

And has a maximum value of .

(Maximum value of T without aliasing).