Question
Download Solution PDFWhat is the convolution of the following two signals?
\(\rm x(t)=\left\{\begin{matrix}1,&-1<t<1\\\ 0,& \rm elsewhere \end{matrix}\right.\) and h(t) = δ(t + 1) + 2δ(t + 2)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven signal
\(\rm x(t)=\left\{\begin{matrix}1,&-1<t<1\\\ 0,& \rm elsewhere \end{matrix}\right.\)
h(t) = δ(t + 1) + 2δ(t + 2)
According to convolution property of impulse
x(t) ⋆ δ(t - t0) = x(t - t0)
∴ x(t) ⋆ h(t) = x(t) ⋆ [δ(t + 1) + 2δ(t + 2)]
= x(t + 1) + 2x(t + 2)
Therefore, correct option is (3)
Last updated on May 28, 2025
-> UPSC ESE admit card 2025 for the prelims exam has been released.
-> The UPSC IES Prelims 2025 will be held on 8th June 2025.
-> The selection process includes a Prelims and a Mains Examination, followed by a Personality Test/Interview.
-> Candidates should attempt the UPSC IES mock tests to increase their efficiency. The UPSC IES previous year papers can be downloaded here.