Let the Laplace transform of a function f(t) which exists for t>0 be F 1 (s) and the Laplace transform of its delayed version f(t – τ) be F 2 (s). Let F 1 * (s) be the complex conjugate of F 1 (s) with the Laplace variable set s = σ + jω. If G (s) = {F_{2} (s) F_{1} ∗ (s) }/{ |F_{1} (s) {{}/{}|} ^{2}}, then the inverse Laplace transform of G(s) is

Correct Answer is : An ideal delayed impulse δ (t – τ)

An ideal delayed impulse δ (t – τ)

An ideal delayed step function u (t – τ)

GATE Electrical Engineering (EE) 2011 Solved Paper

Question : 39 of 65

Marks: +1, -0

Let the Laplace transform of a function f(t) which exists for t>0 be F₁(s) and the Laplace transform of its delayed version f(t – τ) be F₂(s). Let F₁ * (s) be the complex conjugate of F₁(s) with the Laplace variable set s = σ + jω. If

G (s) = \;{F_{2}\;(s)\;F_{1}\;∗\;\;(s)\;}/{\;|F_{1} (s) {{}/{}|} ^{2}}

, then the inverse Laplace transform of G(s) is

An ideal impulse δ (t)
An ideal delayed impulse δ (t – τ)
An ideal step function u (t)
An ideal delayed step function u (t – τ)

Validate

Go to Question:

Prev Question

Next Question