We assume (u(x)=0) in (|x| geq frac{P}{2}). Hence, (tilde{u}(v)) can be sampled at (v_{n}=) (frac{n}{p}), which is

Question:

We assume \(u(x)=0\) in \(|x| \geq \frac{P}{2}\). Hence, \(\tilde{u}(v)\) can be sampled at \(v_{n}=\) \(\frac{n}{p}\), which is enough to know, \(\tilde{u}(v)\) and \(u(x)\) complex. Refer to the following figure. Unfortunately, we do not get \(\{\tilde{u}(v)\}\), but \(\{\tilde{w}(v)\}\), where

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