Question
Download Solution PDFConsider a signal x(t) = u(t - 2) - u (t - 4), evaluate \(\mathop \smallint \limits_{ - \infty }^\infty x(t)\delta (t)dt\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven \(\mathop \smallint \limits_{ - \infty }^\infty x(t)\delta (t)dt\),
x(t) = u(t - 2) - u (t - 4)
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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