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

  1. Jan 5, 2012 #1
    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 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

    Last edited: Jan 5, 2012
  2. jcsd
  3. Jan 5, 2012 #2


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    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?
  4. Jan 10, 2012 #3
    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

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