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Phase of a real number



The Next CEO of Stack OverflowWhat is the difference between phase delay and group delay?How do you relate imaginary numbers with phase shift? How to imagine this?Phase factors for an 32 point fftbaffled by fft phase spectrum!How are phase values able to capture motion from video?In filter design, why isn't it possible to have a frequency response with phase 0?Extracting accurate phase and amplitude information from FFT with an arbitrary number of samplesContinuous phase for phase delay calculus in FIR filtersPhase spectrum of 2D real functionPlotting the Phase Response










1












$begingroup$


Could someone please explain in what case the phase of a real number is equal to -pi (and not pi)?



I know that for positive numbers, the phase is zero. For zero, we define the phase as zero as well. And for negative numbers, the phase would be pi. But I was reading some script and there it says the phase of a real number is either 0, pi, or -pi.






phase







share|improve this question









$endgroup$











  • $begingroup$
    do you know about phase unwrapping?
    $endgroup$
    – robert bristow-johnson
    5 hours ago
















1












$begingroup$


Could someone please explain in what case the phase of a real number is equal to -pi (and not pi)?



I know that for positive numbers, the phase is zero. For zero, we define the phase as zero as well. And for negative numbers, the phase would be pi. But I was reading some script and there it says the phase of a real number is either 0, pi, or -pi.






phase







share|improve this question









$endgroup$











  • $begingroup$
    do you know about phase unwrapping?
    $endgroup$
    – robert bristow-johnson
    5 hours ago














1












1








1





$begingroup$


Could someone please explain in what case the phase of a real number is equal to -pi (and not pi)?



I know that for positive numbers, the phase is zero. For zero, we define the phase as zero as well. And for negative numbers, the phase would be pi. But I was reading some script and there it says the phase of a real number is either 0, pi, or -pi.






phase







share|improve this question









$endgroup$




Could someone please explain in what case the phase of a real number is equal to -pi (and not pi)?



I know that for positive numbers, the phase is zero. For zero, we define the phase as zero as well. And for negative numbers, the phase would be pi. But I was reading some script and there it says the phase of a real number is either 0, pi, or -pi.






phase




phase






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 5 hours ago









NioushaNiousha

1596




1596











  • $begingroup$
    do you know about phase unwrapping?
    $endgroup$
    – robert bristow-johnson
    5 hours ago

















  • $begingroup$
    do you know about phase unwrapping?
    $endgroup$
    – robert bristow-johnson
    5 hours ago
















$begingroup$
do you know about phase unwrapping?
$endgroup$
– robert bristow-johnson
5 hours ago





$begingroup$
do you know about phase unwrapping?
$endgroup$
– robert bristow-johnson
5 hours ago











1 Answer
1






active

oldest

votes


















2












$begingroup$

Or $2pi$, or $3pi$, or any integer multiple of $pi$. Any odd multiple corresponds to -1 + 0i and any even multiple corresponds to 1 + 0i, aka -1 and 1.



"Phase of a real number" is a little bit of a misleading label. What is required here is an understanding of the complex plane and what "phase" means in terms of a DFT bin value.



Your question is equivalent to "For what values of arg(z) is z a real number?"



If that is meaningless to you, I suggest you start by reading two blog articles of mine:



The Exponential Nature of the Complex Unit Circle



And the newest:



Angle Addition Formulas from Euler's Formula



There are of course many other searches. Your terms should be "complex plane real values" for a start.



This is essential foundation material for a lot of DSP concepts.






share|improve this answer











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    1 Answer
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    1 Answer
    1






    active

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    active

    oldest

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    active

    oldest

    votes









    2












    $begingroup$

    Or $2pi$, or $3pi$, or any integer multiple of $pi$. Any odd multiple corresponds to -1 + 0i and any even multiple corresponds to 1 + 0i, aka -1 and 1.



    "Phase of a real number" is a little bit of a misleading label. What is required here is an understanding of the complex plane and what "phase" means in terms of a DFT bin value.



    Your question is equivalent to "For what values of arg(z) is z a real number?"



    If that is meaningless to you, I suggest you start by reading two blog articles of mine:



    The Exponential Nature of the Complex Unit Circle



    And the newest:



    Angle Addition Formulas from Euler's Formula



    There are of course many other searches. Your terms should be "complex plane real values" for a start.



    This is essential foundation material for a lot of DSP concepts.






    share|improve this answer











    $endgroup$

















      2












      $begingroup$

      Or $2pi$, or $3pi$, or any integer multiple of $pi$. Any odd multiple corresponds to -1 + 0i and any even multiple corresponds to 1 + 0i, aka -1 and 1.



      "Phase of a real number" is a little bit of a misleading label. What is required here is an understanding of the complex plane and what "phase" means in terms of a DFT bin value.



      Your question is equivalent to "For what values of arg(z) is z a real number?"



      If that is meaningless to you, I suggest you start by reading two blog articles of mine:



      The Exponential Nature of the Complex Unit Circle



      And the newest:



      Angle Addition Formulas from Euler's Formula



      There are of course many other searches. Your terms should be "complex plane real values" for a start.



      This is essential foundation material for a lot of DSP concepts.






      share|improve this answer











      $endgroup$















        2












        2








        2





        $begingroup$

        Or $2pi$, or $3pi$, or any integer multiple of $pi$. Any odd multiple corresponds to -1 + 0i and any even multiple corresponds to 1 + 0i, aka -1 and 1.



        "Phase of a real number" is a little bit of a misleading label. What is required here is an understanding of the complex plane and what "phase" means in terms of a DFT bin value.



        Your question is equivalent to "For what values of arg(z) is z a real number?"



        If that is meaningless to you, I suggest you start by reading two blog articles of mine:



        The Exponential Nature of the Complex Unit Circle



        And the newest:



        Angle Addition Formulas from Euler's Formula



        There are of course many other searches. Your terms should be "complex plane real values" for a start.



        This is essential foundation material for a lot of DSP concepts.






        share|improve this answer











        $endgroup$



        Or $2pi$, or $3pi$, or any integer multiple of $pi$. Any odd multiple corresponds to -1 + 0i and any even multiple corresponds to 1 + 0i, aka -1 and 1.



        "Phase of a real number" is a little bit of a misleading label. What is required here is an understanding of the complex plane and what "phase" means in terms of a DFT bin value.



        Your question is equivalent to "For what values of arg(z) is z a real number?"



        If that is meaningless to you, I suggest you start by reading two blog articles of mine:



        The Exponential Nature of the Complex Unit Circle



        And the newest:



        Angle Addition Formulas from Euler's Formula



        There are of course many other searches. Your terms should be "complex plane real values" for a start.



        This is essential foundation material for a lot of DSP concepts.







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited 4 hours ago









        MBaz

        9,01041733




        9,01041733










        answered 4 hours ago









        Cedron DawgCedron Dawg

        3,0632312




        3,0632312



























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