GATE EE 2015 Set 1 — Question 20
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Signals & Systems → LTI Systems → Convolution Integral & Sum
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Question
The impulse response of a system, , is as shown in Figure (a). What is the maximum value attained by the impulse response of two cascaded blocks of as shown in Figure (b)?
Correct answer
(D) 1
Solution
The impulse response of two cascaded blocks is the convolution of their individual impulse responses.
Given , which is a unit pulse of height 1 from to .
The total impulse response is:The convolution of two identical rectangular pulses of width and height is a triangular pulse of width and peak height .
Here, and , so the peak height is .
The resulting triangular pulse starts at , reaches its maximum value of 1 at , and ends at .
Thus, the maximum value attained is 1.
Given , which is a unit pulse of height 1 from to .
The total impulse response is:The convolution of two identical rectangular pulses of width and height is a triangular pulse of width and peak height .
Here, and , so the peak height is .
The resulting triangular pulse starts at , reaches its maximum value of 1 at , and ends at .
Thus, the maximum value attained is 1.
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