GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 40 of 65

Marks: +1, -0

Suppose for input

x(t)

a linear time-invariant system with impulse response

h(t)

produces output

y(t)

, so that

x(t) ⊗ h(t)=y(t)

. Further, if

|x(t)| ⊗ y(t)|=z(t)

, which of the following statement is true?

Solution:

By Schwarz inequality

y(t)=∫↙{-∞}↖{∞} x(τ) h(t-τ) d τ

z(t)=∫↙{-∞}↖{∞}|x(τ)| h(t-τ) ∣ d τ

Hence

z(t) ≥ y(t)

for all value of

t

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