Consider a signal x(t) = u(t - 2) - u (t - 4), evaluate \(\mathop \smallint \limits_{ - \infty }^\infty x(t)\delta (t)dt\)

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  1. 8
  2. 0
  3. 4
  4. 2

Answer (Detailed Solution Below)

Option 2 : 0
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Given \(\mathop \smallint \limits_{ - \infty }^\infty x(t)\delta (t)dt\),

x(t) = u(- 2) - (- 4)

F1 Savita Engineering 27-7-22 D5

x(t) =1 ,  when t lies in between 2 and 4

x(t)= 0, in all other cases

The sifting property of the impulse (delta) function is defined as :

\(\mathop \smallint \limits_{ - \infty }^\infty x(t)\delta (t)dt\) = x(0) = 0

The answer is zero.

Option 2 is correct.

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