Consider a signal xt shown in figure belowIf yt-12 xt2 -t-4then the value of y2 is

Given y(t)=12 x ( t2 )*δ (t 4)=12 x ( t 42 )=12 x ( 12t 2 ) at t = 2 y(2)=12 x ( 12(2) 2 )=12 x( 1) Slope of given signal x(t) is 2t x( 1)= 2 y(2)=12( 2 ...

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$Consider a signal x(t) shown in figure below If y (t) = \frac{1}{2} x (\frac{t}{2}) * δ (t - 4) then the value of y(2) is__________$

-1

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Solution

The correct option is A -1
$Given y (t) = \frac{1}{2} x (\frac{t}{2}) * δ (t - 4) = \frac{1}{2} x (\frac{t - 4}{2}) = \frac{1}{2} x (\frac{1}{2} t - 2) at t = 2 y (2) = \frac{1}{2} x (\frac{1}{2} (2) - 2) = \frac{1}{2} x (- 1) Slope of given signal x(t) is 2t x (- 1) = - 2 y (2) = \frac{1}{2} (- 2) = - 1$

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Consider a signal x(t) shown in figure belowIfy(t)=12 x(t2)∗δ(t−4)then the value of y(2) is__________ -1

The correct option is A -1 Giveny(t)=12 x(t2)∗δ(t−4)=12 x(t−42)=12 x(12t−2)at t = 2y(2)=12 x(12(2)−2)=12 x(−1)Slope of given signal x(t) is 2tx(−1)=−2y(2)=12(−2)=−1

$Consider a signal x(t) shown in figure below If y (t) = \frac{1}{2} x (\frac{t}{2}) * δ (t - 4) then the value of y(2) is__________$

-1