Cp. Sonett, MULTIRATE ALIAS FROM PERIODICALLY INTERRUPTED SAMPLING OF TIME-SERIES- IS THE QBO-SOLAR ACTIVITY CYCLE OF NORTH POLAR TEMPERATURE AN EXAMPLE, Annales geophysicae, 11(6), 1993, pp. 498-501
Intermittent sampling of a time series, wherein a basic uniform sampli
ng rate is interrupted by a switch which periodically turns the sampli
ng on and off, defines two sampling rates and two Nyquist periods, N1
and N2, respectively twice the shorter and longer periods of sampling.
Thus, if data sampled in this manner contains frequencies higher than
1/N2 (that of the interruption switch), alias of the spectrum takes p
lace even though N1 may be of sufficiently high frequency to itself sa
tisfy the nominal single sampler Nyquist criterion. This condition can
lead to potentially gross misinterpretation of the true frequency spe
ctrum. This paper formalizes the problem for the frequency domain, fol
lowed by exploration of the possibility that such a corrupting effect
may be present in the QBO-solar cycle relation reported by Labitzke an
d coworkers.