Begin with the real periodic-TO signal x(t). That is. x(t) = x(t + To). The Four

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Begin with the real periodic-TO signal x(t). That is. x(t) = x(t + To). The Fourier series coefficients for x(t) are {Cn, n = . . . , - 1,0,1,2, ...}. Prove or disprove each of t he following claims: If x(t) is even, the Fourier series coefficients {Cn, n = . . . , - 1,0,1,2, ...} are real. If x(t) is odd, the Fourier series coefficients {Cn, n = . . . , - 1,0,1,2, ...} are imaginary. If x(t) has even half-wave symmetry, meaning x(t) = x(t + T0/2), the odd indexed Fourier series coefficients {Cn, n = . . . , - 1,0,1,2, ...} are zero. If x(t) has odd half-wave symmetry, meaning -x(t) = x(t + T0/2), The even indexed Fourier series coefficients {Cn, n = . . . , - 1,0,1,2, ...} are zero. The Fourier series coefficients for the real signal ar(-t) are {Cn, n = . . . , - 1,0,1,2, ...}.

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