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after doing a complex fourier series on a function. i am asked to find and graph the magnitude and phase spectrum of a fucntion.

now to cut the long story short. let's say we arrived a fourier series like this.

= [itex]\sum_{i=-∞}^{∞}[/itex] [itex]\frac{1}{npi}[/itex]sin [itex]\frac{npi}{2}[/itex]exp(jnpit)

so [itex]c_{n}[/itex] = [itex]\frac{1}{npi}[/itex]sin [itex]\frac{npi}{2}[/itex]

= the phase spectrum of a function is the phase of [itex]c_{n}[/itex], but notice that this is PURELY REAL like this.

=[itex]\frac{1}{npi}[/itex]sin [itex]\frac{npi}{2}[/itex] + j *(0)

= phase is found as [itex]tan^{-1}[/itex] ( [itex]\frac{0}{[itex]\frac{1}{npi}[/itex]sin [itex]\frac{npi}{2}[/itex]}[/itex] )

= now is it not supposed to be zero for all n. but this function has a phase plot

= please explain to me how they did this,

my idea is that when we look at the complex plane.POSITIVE REAL part has angle 0 while NEGATIVE REAL part has 180 OR -180(I AM NOT SURE WHICH).

= please explain to me how [itex]tan^{-1}[/itex] 0/anything is accepted. AND which angle to choose 180 or -180

THANKS A LOTTTTTTTTTTTTTTTTTTTTTTT.....!!!

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# Homework Help: WHAT IS THIS Phase Spectrum of this function.

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