\left \{ x(n) \right \} is a real-valued periodic sequence with a period N.\, x(n) and X(k) form N-point Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence
y(n) = \frac{1}{N} \sum_{r=0}^{N-1} x(r) x(n + r) is
(a) |X(K)|^{2}
(b) \frac{1}{N} \sum_{r=0}^{N-1} X(r) X^{*} (k + r)
(c) \frac{1}{N} \sum_{r=0}^{N-1} X(r) X (k + r)
(d) 0