⁽²⁾A simple proof of this fact can be outlined using multirate signal processing. Assume the spectrum G(e^jω) is nonzero only over [-ω _b,ω_b], for ω_b < π∕K; g[n] can therefore be subsampled by at least a factor of K without aliasing, and the support of the resulting spectrum is going to be [-Kω_b,Kω_b], with Kω_b < π. However, g[Kn] = δ[n], whose spectral support is [-π,π].