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How to find the argument of a function?

  1. Jun 2, 2015 #1
    1. The problem statement, all variables and given/known data
    IMG_20150601_210114.jpg
    For the function ##V(f) = A \tau sinc(f \tau)## in the picture how do you conclude that the argument of ##V(f)## is 0º, +180º or -180º?

    2. Relevant equations
    ##arg = arctan({\frac{Im}{Re}})##

    3. The attempt at a solution
    The upper graphic represents the absolute value of the function, right? I understand that being a sinc function the negative parts of the graphic should "jump" to the positive side. I also understand why the function return 0 on k/τ.
    Is it correct to think, for example, between 1/τ and 2/τ the sinc function returns negative values but because it needs to shift to the positive values the fase should be negative so that negative times negative = positive?
    I'm so sorry if this questions sounds too basic. I'm trying to learn by myself, I'm not attending any classes and I have no one to ask this kind of doubts.
    Thanks in advance.
     
    Last edited: Jun 2, 2015
  2. jcsd
  3. Jun 2, 2015 #2
    Write analytical ##sinc()## function and think about ##sin()## that you know much better.
     
  4. Jun 2, 2015 #3
    ##sinc(x) = {\frac{\sin(\pi x)}{\pi x}}##

    Capture.jpg
    The ##sin()## is positive between ##-2 \pi## and ##- \pi## and between ##0## and ##\pi## and is negative between ##- \pi## and ##0## and between ##\pi## and ##2 \pi##...
     
  5. Jun 2, 2015 #4
    On your function the argument is ##ft## so ##f=\pi##. What must be ##Α## in your function?
     
  6. Jun 2, 2015 #5
    ##A## represents the amplitude of the function, the value that the function return when ##x = 0##
     
  7. Jun 2, 2015 #6
    I think ##A## has only a sign. The second diagram is a step function. Make some diagrams.
     
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