The symmetries of the Fourier transform are quite useful. In Section 11-5.2, the conjugate-symmetry property was used to show that for a real x(t) the real part of its transform is even and the imaginary part is odd. For this problem, assume that is a real signal with Fourier transform, X(jω).
(a) Prove that the magnitude |X(jω)| is an even function of ω; i.e., |X (–jω)| = |X (jω)|.
(b) Prove that the phase < X (jω) is an odd function of ω i.e., <X(-j ω) = –< X (jω).
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