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Math Help - Finding the norm of a complex exponential

  1. #1
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    Finding the norm of a complex exponential

    I am not sure if this is the topic to cite my query.Anyway,

    I have to find the 1-norm,2-norm and the ∞- norm of any discrete-time finite-duration complex exponential
    φk = e^(2πj kn/N) , for any k = 0, . . . , N − 1.
    ////
    I found the 2-norm but I have not understand well the 1-norm and particularly the infinite norm.. Is it true that the 1-norm is equal to the sum of the absolute value of a discrete signal (x(n)), for n=0 to N-1 ?
    Could someone give me a help here?How do I find the norms of φk ?

    thanks in advance..
    Last edited by tsebamm; October 31st 2010 at 04:47 AM. Reason: rectify
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  2. #2
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    Is it true that the 1-norm is equal to the sum of the absolute value of a discrete signal (x(n)), for n=0 to N-1 ?
    Yes. See p-norm in Wikipedia.
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  3. #3
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    Quote Originally Posted by emakarov View Post
    Yes. See p-norm in Wikipedia.
    Yes, i have already sawn that. Thanks for your response. Do you have any idea about the infinite form? I've checked the definition of it, but I can't put it in my case here.
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  4. #4
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    What exactly are you asking about the infinite case? The space \ell_p (see here) is the space of infinite sequence with p-norm. What are the sequence elements? I don't think the finite sequence e^(2\pi k/N), k=0,\dots,n-1, repeated infinite number of times is in \ell_p for finite p because 1 occurs infinitely far in this sequence. It is in \ell_\infty, though.
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