Solution 7
(a) Given:
![](Solution_Template2_clip_image002_0000.gif)
![](Solution_Template2_clip_image004_0000.gif)
The Fourier transform of [where a>0] is .
So Fourier transform of x(t) is
![](Solution_Template2_clip_image010_0000.gif)
Similarly, the Fourier transform of output y[t] is
![](Solution_Template2_clip_image012_0000.gif)
Let the frequency response of the given LTI system be .
So, by the convolution theorem,
As ,
![](Solution_Template2_clip_image018_0000.gif)
![](Solution_Template2_clip_image020_0000.gif)
By solving this, we get
![](Solution_Template2_clip_image022_0000.gif)
![](Solution_Template2_clip_image024_0000.gif) ![](Top.gif)
(b) By taking Inverse Fourier Transform of , we get
![](Solution_Template2_clip_image026_0000.gif) ![](Top.gif)
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