Consider the following problems related to the modulation and power properties of the Fourier transform. (a) The

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Consider the following problems related to the modulation and power properties of the Fourier transform.

(a) The carrier of an AM system is cos(10t), consider the following message signals

i. m(t) = cos(t)

ii. m(t) = r(t) ˆ’ 2r(t ˆ’ 1) + r(t ˆ’ 2),               where r(t) = tu(t)

Sketch the modulated signals y(t) = m(t) cos(10t) for these two messages and find their corresponding spectrum.

(b) Find the power Px of a sinc signal x(t) = sin(0.5t)/(Ï€t), i.e., the integral

ког а |x(t)l*dt |Pк -00

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