The harmonic analysis of certain multiplicative processes of the formg(t)X(t)is considered, wheregis a deterministic function, and the stochastic processX(t)is of the formX(t)=\sum X_{n}l_{[n \alpha , (n+l) \alpha]}(t), where a is a positive constant and theX_{n}, n=0, \pm 1,\pm 2, \cdotsare independent and identically distributed random variables with zero means and finite variances. In particular, we show that if g is Riemann integrable and periodic, with period incommensurate with\alpha, theng(t)X(t)has an autocovariance in the Wiener sense equal to the product of the Wiener autocovariances of its factors,C_{gx} = C_{g}C_{x}. Some important cases are examined where the autocovariance of the multiplicative process exists but cannot be obtained multiplicatively.