Spectral representation of stationary processes. The Wold decomposition theorem roughly states that any stationary stochastic process can be decomposed into at most two components consisting of (1) a deterministic (as defined in one of the first lectures) and (2) a non-deterministic process. Consider the simple case where the process decomposes into two components: a harmonic process (with 3 different frequencies f1, f2 and f3; same power in each) and an AR(1) process. Which of the two components is deterministic? Why? Which of the two components contribute to the discrete and continuous part of the spectrum? Draw a sketch of the corresponding two-sided (negative and positive frequencies) power spectrum of the original process.

Please draw a sketch in your hand and upload a figure here.