Thread: 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..

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.

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.

What exactly are you asking about the infinite case? The space (see here) is the space of infinite sequence with p-norm. What are the sequence elements? I don't think the finite sequence , , repeated infinite number of times is in for finite because 1 occurs infinitely far in this sequence. It is in , though.