Fourier Transform Question - Negative Frequencies?

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J$C

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When I see a graph of a Fourier Transform, or something in the frequency domain, say band-limited from -[tex]\Omega[/tex] to [tex]\Omega[/tex], I'm confused to what the interpretation is of the negative frequencies. Physically it would seem as though something considered in cycles/second for example, should be positive but mathematically the FT will allow for negative frequencies.

Can somebody clarify this for me?
 

HallsofIvy

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[tex]e^{-\omega ix}= e^{\omega (-i)x}[/tex] so negative frequencies are just the complex conjugate of the positive frequencies.
 
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Hadn't really thought about it. Physically positive/negative frequencies could be interpreted as left/right circularly polarized waves.
 

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