I have the following task:
Assume that $h$ is a filter with finite support $[0..(m−1)]$ for some $m>0$. Let $x$ be a circular extension of $h$.
- Prove that $x\in l_\infty$.
- When is $x\in𝑙_1 $?
- Build a filter $y\in 𝑙_1 $ such that its periodized version $y^m$ equals to $x$ on signals with period $m$.
I answered two first questions but cannot figure out the solution for building filter $y\in l_1$ such that its periodized version $𝑦^𝑚$ equals to $x$ on signals with period $m$.
Could someone help me?