# Thread: Finding the norm of a complex exponential

1. ## 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.
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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 ?

2. 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.

3. Originally Posted by emakarov
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.

4. What exactly are you asking about the infinite case? The space $\displaystyle \ell_p$ (see here) is the space of infinite sequence with p-norm. What are the sequence elements? I don't think the finite sequence $\displaystyle e^(2\pi k/N)$, $\displaystyle k=0,\dots,n-1$, repeated infinite number of times is in $\displaystyle \ell_p$ for finite $\displaystyle p$ because 1 occurs infinitely far in this sequence. It is in $\displaystyle \ell_\infty$, though.