How can you read the phase spectra from a Fourier Transform?(adsbygoogle = window.adsbygoogle || []).push({});

if [tex]g(t) = Sin(2\pi f_{c}t)[/tex]

then for the single sided spectrum, you have one frequency component at [tex]f=f_{c}[/tex] with a height of [tex]\frac{1}{j}[/tex] which from looking at the complex plane, corresponds to a phase of [tex]\frac{\pi }{2}[/tex] (ie. [tex]g(t) = Sin(2\pi f_{c}t)[/tex] is made up of a cosine component with [tex]f=f_{c}[/tex] and phase = [tex]\frac{\pi }{2}[/tex].

But, if you consider [tex]\frac{1}{j} = -j[/tex], then the phase would correspond to [tex]\frac{3\pi }{2}[/tex] which would in effect negate the amplitude ([tex]Cos(x - \frac{3\pi }{2}) = -Cos(x - \frac{\pi }{2})[/tex].

So which complex amplitude should be considered correct?[tex]\frac{1}{j} or -j[/tex] ?

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# Phase Spectra from Fourier Transform

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