For any integer N > 0, consider the set of points 2;= 2π) j = 0,...,N-1, (2.1.24) N referred to as nodes or grid points or knots. The discrete Fourier coefficients of a complex-valued function u in (0,21] with respect to these points are N-1 ūk = k=-N/2, ...,N/2-1. N (2.1.25) j=0 Due to the orthogonality relation I u(x;)e-ika; ? 1 2 N-1 1 N j=0 Σ e-ipt; == ={ if p = Nm, m = 0, +1, #2, ... otherwise,