=+11. For 0 ≤ m ≤ n − 1 and a periodic function f(x) on [0,1], define the sequence bm = f(m/n). If ˆbk is the finite Fourier transform of the sequence bm, then we can approximate f(x) by n/2

k=−n/2

ˆbke2πikx.

Show that this approximation is exact when f(x) is equal to e2πijx, cos(2πjx), or sin(2πjx) for j satisfying 0 ≤ |j| < n/2.