Electronics and Communication Engineering - Exam Questions Papers - Discussion
Discussion Forum : Exam Questions Papers - Exam Paper 7 (Q.No. 39)
39.
Consider Continuous time system y(t) = 
x(t) - 
. For the system to be linear response ax1(t) + bx2(t) should be ay1(t) + by2(t) with relation between constant 'a' and 'b' as __________ .
x(t) - . For the system to be linear response ax1(t) + bx2(t) should be ay1(t) + by2(t) with relation between constant 'a' and 'b' as __________ .Answer: Option
Explanation:
Let ax1(t) + bx2(t) = m(t)
where m(t) is new input which causes the output n(t)
n(t) = m(t) -
n(t) = {ax1(t) + bx2(t)} -
add and subtract
n(t) = 
x1(t) -a + 
x2(t) -b +a +b -
n(t) =
+{a + b - 1}
n(t) = ay1(t) + by2(t) +{a + b - 1}
For linearity, n(t) = ay1(t) + by2(t)
∴ {a + b - 1} = 0 ∴ a + b = 1.
Discussion:
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