Solution 8
(a) We know that
![](Solution_Template6_clip_image002_0000.gif)
is a periodic square wave of period .
With as shown in the figure.
![](Solution_Template6_clip_image009.gif)
Figure (a)
We calculate as follows: (FT of a periodic signal)
![](Solution_Template6_clip_image013.gif)
where,
![](Solution_Template6_clip_image015.gif)
Considering any one period , (say from 0 to ) and
Substituting ![](Solution_Template6_clip_image018.gif)
![](Solution_Template6_clip_image020.gif) ![](Solution_Template6_clip_image022.gif)
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
![](Solution_Template6_clip_image002_0001.gif)
is a periodic square wave of period .
With as shown in the figure.
![](Solution_Template6_clip_image009_0000.gif)
Figure (b)
We calculate as follows: (FT of a periodic signal) ![](Solution_Template6_clip_image013_0000.gif)
where
![](Solution_Template6_clip_image015_0000.gif)
Considering any one period , (say from 0 to T) and
Substituting ![](Solution_Template6_clip_image018_0000.gif)
![](Solution_Template6_clip_image037.gif)
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).![](Top.gif)
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