The sinusoidal signal x(t) = 3 cos(200t + 7/6) is passed through a square-law device defined by the input-output relation y{t) = x²(t) Using the trigonometric identity cos²0 = }(cos 20 + 1) %3D show that the output y(t) consists of a dc com- ponent and a sinusoidal component. (a) Specify the dc component. (b) Specify the amplitude and fundamental fre- quency of the sinusoidal component in the output y(t).

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EENG226 SIGNALS AND SYSTEMS
The sinusoidal signal
x(t)
= 3 cos(200t + 7/6)
is passed through a square-law device defined by
the input-output relation
y{t) = x²(t)
Using the trigonometric identity
cos²0 = {(cos 20 + 1)
%3D
show that the output y(t) consists of a dc com-
ponent and a sinusoidal component.
(a) Specify the dc component.
(b) Specify the amplitude and fundamental fre-
quency of the sinusoidal component in the
output y(t).
Transcribed Image Text:The sinusoidal signal x(t) = 3 cos(200t + 7/6) is passed through a square-law device defined by the input-output relation y{t) = x²(t) Using the trigonometric identity cos²0 = {(cos 20 + 1) %3D show that the output y(t) consists of a dc com- ponent and a sinusoidal component. (a) Specify the dc component. (b) Specify the amplitude and fundamental fre- quency of the sinusoidal component in the output y(t).
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