Frequency mixing
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Why is that if one multiplies a function say g(t) by exp(jwt) in matlab, the frequency resulting signal is upconverted rather for it to be downconverted. mathematically by Fourier analysis; FT-means Fourier transform say g(t)=sin(wt) if FT[g(t)]=G(wo) then FT[g(t)exp(jwt)]= G(wo+w), but in matlab the plotting abs(FT[g(t)exp(jwt)]) gives a result that presents FT[g(t)exp(jwt)]=G(wo-w) Pls, kindly shed light on this!
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Wayne King
2011-10-28
0 个投票
Let X(\omega) = G(\omega-\omega_0)
Then
X(\omega_0) = G(0)
if \omega_0 is positive, then X(\omega) is shifted to the right of G(\omega)
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Wayne King
2011-10-28
0 个投票
Multiplying a signal g(t) by e{j\omega_0 t} shifts the spectrum to the right by \omega_0
G(\omega-\omega_0)
not G(\omega+\omega_0)as you indicate above.
The Fourier transform of g(t)e{j\omega_0 t} is G(\omega-\omega_0)
2 个评论
Wayne King
2011-10-28
G(\omega+\omega_0) is the Fourier transform of g(t)e{-j\omega_0 t}
Bayus
2011-10-28
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