A periodic signal x(t), of fundamental frequency Ω 0 = Ï, has a period The signal x(t)

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A periodic signal x(t), of fundamental frequency Ω0= π, has a period

1+t -1 <t < 0 1-t 0<t< 1, x1 (t) =

The signal x(t) is the input of an ideal low-pass filter with the frequency response H(jΩ) shown in Figure 4.20. Let y(t) be the output of the system.

(a) Determtine the Fourier series coefficients needed to find the output y(t) of the filter.

(b) Is the output signal y(t) periodic? If so, determine its fundamental period T0, and its dc value.

(c) Provide the constants A,B, and C in the output: y(t) = A + B cos(Ï€ t + C).


Figure 4.20:

Η (Ω) ZH (jN) п/2 Ω Ω -1.5π 1.5π - π/2 2.

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