Compute the spectral density of terms

Question

Assignment:

Suppose we are given a stationary mean-zero series X_t with spectral density f_X (ω) (note that X_t is not necessarily a white noise),and we then construct a new series Y_t by Y_t=a Y_t-1+X_t with |a|< 1. Compute the spectral density of Y_t in terms of f_X(ω) and a.