à o MM 
The synoptic sequence retrieved from the "unfiltered" asynoptic 
observations is shown in Fig. 4. Despite the unresolvable Spectra] content, 
and accompanying aliasing, the structure and evolution are recovered with 
reasonable fidelity. In fact, the fields are quite faithful except at the 
initial and final map times. 
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Fig. 4 As for Fig. 2 but for an eastward traveling wavenumber 1 mode, whose amplitude decays exponentially in ori 
time. Synoptic evolution is faithfully retrieved within the sample interval. However unresolvable cyc 
frequencies contaminate the mape at the beginning and end of the sample period. 
This discrepancy is readily seen in the evolution of wavenumber ] 
amplitude (Fig. 5). Within the sample interval, the synoptic retrieval 
adheres closely to the true evolution. The error over the interior appears 
as a small oscillation, and results from unresolvable frequency content. At 
the ends, however, the amplitude departs substantially from the true behavior. 
This is clearly understood once it is recognized that the true behavior over 
the sample interval, is implicitly extended periodically (c.f., Fig. 5). 
Discontinuities are introduced when the initial and final values of y do 
not coincide. In such cases, the Fourier expansion converges to the midpoint 
of the discontinuity (open circles).. 
150 
EI E MOL oai