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8. Given a Fourier transform pair f(@) = F[f (t)] = f(t)e-lot dt (Forward transform) and f(t) = S* F[f(t)]e*iet dw = L f(@)e*il* dw (Inverse transform), show that the Fourier {1 if-

8. Given a Fourier transform pair f(@) = F[f (t)] = f(t)e-lot dt (Forward transform) and f(t) = S* F[f(t)]e*iet dw = L f(@)e*il* dw (Inverse transform), show that the Fourier {1 if-

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8. Given a Fourier transform pair f(@) = F[f (t)] = S f(t)e-lot dt (Forward transform) and f(t) = L** F[f(t)]etiet do = S** f(@)e*iot do (Inverse transform), show that the Fourier (1 if-<t<+ (o transform of the box function defined as rect(t) = is F[rect (t)] = otherwise sin = sinc ), a = 2nf.
Transcribed Image Text:8. Given a Fourier transform pair f(@) = F[f (t)] = S f(t)e-lot dt (Forward transform) and f(t) = L** F[f(t)]etiet do = S** f(@)e*iot do (Inverse transform), show that the Fourier (1 if-<t<+ (o transform of the box function defined as rect(t) = is F[rect (t)] = otherwise sin = sinc ), a = 2nf.
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