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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) − 2r(t−1) + r(t−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)/(πt), i. e. , the integral Px = ∫−∞∞ |x(t)|2 dt

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) − 2r(t−1) + r(t−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)/(πt), i. e. , the integral Px = ∫−∞∞ |x(t)|2 dt

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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 ⁡ ( 10 t ) , consider the following message signals i. m ( t ) = cos ⁡ ( t ) ii. m ( t ) = r ( t ) − 2 r ( t − 1 ) + r ( t − 2 ) , where r ( t ) = t u ( t )
Sketch the modulated signals y ( t ) = m ( t ) cos ⁡ ( 10 t ) for these two messages and find their corresponding spectrum. (b) Find the power P x of a sinc signal x ( t ) = sin ⁡ ( 0.5 t ) / ( π t ) , i.e., the integral
P x = ∫ − ∞ ∞ | x ( t ) | 2 d t

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