Figure 4.

Behavior of $|{\lambda }_{0,n}^{2c}|$for c = πL (Nyquist sampling) and several values of L. For each value of L, the dotted vertical line represents n = 2c/π, and the dashed vertical line represents the first index n for which $|{\lambda }_{0,n}^{2c}|\le {10}^{-12}$, which we denote by $n_1^{2c}$. First, we observe that 2c/π is the exact index for which $|{\lambda }_{0,n}^{2c}|$ begins its rapid decay, and, second, it is evident that the difference between $n_1^{2c}$ and the estimate 2c/π grows extremely slowly with L, making the asymptotic estimate $n_1^{2c}~2c/\pi$ sufficiently accurate even for moderate values of L.