Phase of a real number












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







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$endgroup$












  • $begingroup$
    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




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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






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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.






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    $begingroup$

    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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