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Fourier Transform The modulation property of the Fourier transform. (a) Let f(t) be a signal, s0 a number, and define g(t) = f(t)cos⁡(2πs0t). Show that Fg(s) = 1 2 Ff(s − s0) + 1 2 Ff(s + s0) (b) Find the signal (in the time domain) whose Fourier transform is pictured, below.

Fourier Transform The modulation property of the Fourier transform. (a) Let f(t) be a signal, s0 a number, and define g(t) = f(t)cos⁡(2πs0t). Show that Fg(s) = 1 2 Ff(s − s0) + 1 2 Ff(s + s0) (b) Find the signal (in the time domain) whose Fourier transform is pictured, below.

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Fourier Transform
  1. The modulation property of the Fourier transform. (a) Let f ( t ) be a signal, s 0 a number, and define
g ( t ) = f ( t ) cos ⁡ ( 2 π s 0 t ) .
Show that
F g ( s ) = 1 2 F f ( s − s 0 ) + 1 2 F f ( s + s 0 )
(b) Find the signal (in the time domain) whose Fourier transform is pictured, below.

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