WHAT IS THIS Phase Spectrum of this function.

[jose_peeter]

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.

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

so c_{n} = \frac{1}{npi}sin \frac{npi}{2}

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

=\frac{1}{npi}sin \frac{npi}{2} + j *(0)

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

= 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 tan^{-1} 0/anything is accepted. AND which angle to choose 180 or -180

THANKS A LOTTTTTTTTTTTTTTTTTTTTTTT...!

 

[LCKurtz]

I'm not sure about the term "phase spectrum". If it means frequency spectrum, isn't that just a plot of $|c_n|$ against $\omega_n$? Or is it something else?

 

[jose_peeter]

I mean the graph of the PHASE against the frequency what you have suggested is the magnitude against frequency.

when you do it. please don't just show the graph, i know the answer but don't understand how to get it.
my doubts and questions i have asked in previous post above

thanks