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GATE 2015 EE – Question 20

Signals and Systems · Linear time invariant and causal systems · 1 mark · Multiple choice

The impulse response $g(t)$ of a system, $G$, is as shown in Figure (a). What is the maximum value attained by the impulse response of two cascaded blocks of $G$ as shown in Figure (b)?

(a) $g(t)$ is a rectangular pulse of height 1 from $t = 0$ to $t = 1$. (b) Two copies of the block G connected in cascade.
  1. $\frac{2}{3}$
  2. $\frac{3}{4}$
  3. $\frac{4}{5}$
  4. 1

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Correct answer: (D) 1

Explanation

The impulse response of two cascaded systems is the convolution of the two impulse responses. Convolving a unit pulse of width 1 with itself gives a triangle from 0 to 2 whose peak height is 1, at $t = 1$.