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निम्नलिखित दो सिग्नलों का कनवल्शन क्या है?

\(\rm x(t)=\left\{\begin{matrix}1,&-1 और h(t) = δ(t + 1) + 2δ(t + 2)

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UPSC IES Electrical 2022 Prelims Official Paper
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  1. y(t) = x (t + 1) + 2x (t - 2)
  2. y(t) = x (t - 1) + 2x (t + 2)
  3. y(t) = x (t + 1) + 2x (t + 2)
  4. y(t) = x (t - 1) + 2x (t - 2)

Answer (Detailed Solution Below)

Option 3 : y(t) = x (t + 1) + 2x (t + 2)
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दिया गया सिग्नल

\(\rm x(t)=\left\{\begin{matrix}1,&-1

F1 Madhuri Engineering 10.05.2022 D1

h(t) = δ(t + 1) + 2δ(t + 2)

F1 Madhuri Engineering 10.05.2022 D2

आवेग के कनवल्शन गुण के अनुसार

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)

इसलिए, सही विकल्प (3) है

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