Thread Subject: Frequency mixing

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!

"Bayus" wrote in message <j8dusj$8hq$1@newscl01ah.mathworks.com>...
> 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!

Hi,

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)