- #1
jose_peeter
- 8
- 0
dear all,
after doing a complex Fourier series on a function. i am asked to find and graph the magnitude and phase spectrum of a function.
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...!
after doing a complex Fourier series on a function. i am asked to find and graph the magnitude and phase spectrum of a function.
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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