Fourier Series and Parseval\'s Relation. Consider a signal x(t) that has the fol

Question

Fourier Series and Parseval's Relation. Consider a signal x(t) that has the following properties: x(t) is periodic with T_0 = 4 x(t) has a DC component of 1/2 x(t) is real and offsetting x(t) by its DC component makes it an odd signal (i.e. signal x(t) = x(t) - 1/2 is real and odd, therefore c_1 = -c_-1) The only non-zero FS coefficients of x(t) are C_0, C_1, and c_-1 1/T_0 Integral_T_0 |x(t)|^2dt = 3/4 Deduce as much as possible about x(t) using FS properties and Parseval's relation for periodic signals. Show that x(t) can be either x(t) = 1/2 - sin(pi t/2) or x(t) = 1/2 + sin(pi t/2)

Explanation / Answer

x(t)=1/2-sin(pit/2)

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