Finding 2-Norm of Weighted Sum of Complex Exponentials

[tsebamm]

Hi,

Homework Statement

We have a signal y(n) which is the weighted sum of two complex exponentials
y(n)=A*φk(n)+Β*φl(n)

k different to l
A,B are complex constants

I have to find the 2-norm of y(n). Can anyone help me with that?
Am I going to solve it with parseval's theorem?

Homework Equations

φκ=exp(2πjkn/N)
φl=exp(2πjln/N)

Thanks in advance,

Nikolas

 

[fzero]

You might want to define what you mean by 2-norm. Is it the $$\ell^2$$ norm, where the $$\varphi_k(n)$$ are viewed as (perhaps elements of) sequences? Or is it the $$L^2$$ norm where the $$\varphi_k(n)$$ are functions of $$n$$? If it's the latter, you can use Parseval's theorem. In either case, your norm is going to include the norm on $$\mathbb{C}$$,

$$|x| = \sqrt{ x^*x }.$$