4. The Fourier transform of a signal g(t) is denoted by G(f). Show that: (a) If...

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4. The Fourier transform of a signal g(t) is denoted by G(f). Show that: (a) If a real signal g(t) is an even function of time t, then G(f) is purely real. If the real signal g(t) is an odd function of time t, then G(f) is purely imaginary. (b) 1"g(t)=()"G(") (f), where G(") (f) is the n'h derivative of G(f) with respect to f. (c) "g(t)dt = ()"G(") (0) 4. The Fourier transform of a signal g(t) is denoted by G(f). Show that: (a) If a real signal g(t) is an even function of time t, then G(f) is purely real. If the real signal g(t) is an odd function of time t, then G(f) is purely imaginary. (b) 1"g(t)=()"G(") (f), where G(") (f) is the n'h derivative of G(f) with respect to f. (c) "g(t)dt = ()"G(") (0)

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a If gt is an even function of time then we have gt gt for all t The Fourier transform of gt is give... View the full answer