 Solution

The consistent matching is:

Series C stops after about six months, identifying machine 2. Its short record gives spectrum W a coarser Fourier frequency resolution. Series A resolves the annual variation but misses the changing daily phase: the regular three-day interval samples the daily oscillation at the same phase, so its daily contribution aliases to a constant. Its spectrum is Y. Machine 3 produces the half-daily-frequency alias in X, leaving D as its time series. The fully sampled two-year record B and spectrum Z agree with the supplied first row.

These identifications use the record lengths, frequency locations and sampling intervals. They do not require assuming that the plotted spectral heights have an identical normalization.