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.










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.










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.










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






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











$endgroup$














    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "295"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fdsp.stackexchange.com%2fquestions%2f56336%2fphase-of-a-real-number%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    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






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Signal Processing Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fdsp.stackexchange.com%2fquestions%2f56336%2fphase-of-a-real-number%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            Popular posts from this blog

            الفوسفات في المغرب

            Four equal circles intersect: What is the area of the small shaded portion and its height

            جامعة ليفربول