For each case given below, tell whether the given function can be a satisfactory auto correlation function. If it is not satisfactory, give the reason(s).

(a) R_a (τ) = II (τ/τ₀) where τ₀ is a constant;

(b) R_b (τ) = A (τ /τ₀) where τ₀ is a constant;

(c) R_c (τ) = A cos (2πf₀τ) where A and f₀ are constants;

(d) R_d (τ) = A + B cos (2πf₀τ) where A, B, and f₀ are constants;

(e) R_e (τ) = A sin (2πf₀τ) where A and f₀ are constants;

(f) R_f (τ) = A sin² (2πf₀τ) where A and f₀ are constants;