  By introducing $X^{ls}(t)$ as a random mixture of two stationary processes
where the time dependent random weights have exponentially convex covariance,
we show that this process has a multi-component locally stationary covariance
function in Silverman's sense. We also define $X^p(t)$ as a certain continuous
time periodically correlated (PC) process where its covariance function is
generated by the covariance function of a discrete time through defining some
simple random measure on real line. We also impose a bi-periodic correlation
for this PC process with $X^{ls}(t)$. The existence of such random measure is
proved. Then by defining $X(t)=X^{ls}(t)+X^p(t)$ as a certain periodically
correlated multi-component locally stationary process, the covariance structure
and time varying spectral representation of such processes are characterized.
