# Sinusoidal signal x (t) = 4cos (200t + $\frac{π}{6}$) is passed through a square law device defined by the input output relation y (t) = x^2(t). The DC component in the signal is _____________

+1 vote
Sinusoidal signal x (t) = 4cos (200t + $\frac{π}{6}$) is passed through a square law device defined by the input output relation y (t) = x^2(t). The DC component in the signal is _____________

(a) 3.46

(b) 4

(c) 2.83

(d) 8

This question was posed to me by my school principal while I was bunking the class.

The origin of the question is Characterization and Nature of Systems topic in section Laplace Transform and System Design of Signals and Systems

by (42.1k points)
The correct option is (d) 8

The explanation is: y (t) = 4^2 cos^2 (200t + $\frac{π}{6}$)

= $4^2 \frac{(1+cos⁡2(200t + \frac{π}{6}))}{2}$

= 8 + 8 cos (400t + $\frac{π}{3}$)

Hence, DC component = 8

AC component = 8 cos (400t + $\frac{π}{3}$).

+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote
+1 vote