tic 
ntent, 
ith 
, the 
1:2.0 
  
ars 
At 
lavior. 
over 
| 
point 
md 
I E MC Wr am 
ee cn RE EE ec 
  
I | 
09 74, 
08 N 
07 S 
06 
0.5 
04 
03 
0.2 7 
01 " 
A us 
-40 -30 -20 -10 O 
t 
Fig. 5 Temporal evolution of wave L amplitude at -80° latitude: true (solid), 
synoptic retrieval (dashed). True evolution is faithfully recovered 
within the sample interval, but at the ends the synoptic retrieval 
approaches the midpoint of discontinuity generated in periodic extension. 
Ivi 
     
   
—— — Periodic Extensio 
== === Synoptic Retrieval 
| | 
  
  
  
10 20 30 40 
This behavior, known as Gibb's phenomena, is responsible for most 
of the high frequency content in (2). It is the sharp corners at the 
discontinuities which require the higher components, not the smooth evolution 
within the sample. The discrepancy is an annoyance, but nothing more. It 
can be readily avoided by a simple application of "windowing." If the 
sample is extended on each end by a taper, arbitrarily falling to zero, the 
periodic extension contains no discontinuities, and hence no "spurious" high 
frequency content. 
Consider the field (2) over |t| < 2.0. The evolution is comple- 
mented, crudely, on either end by simple cosine taper, dropping to zero in 
1 day. Despite its unrefined character, e.g., the sharp transition at 
t = + 2.0 (c.f., Fig. 6), this simple extension appears to be quite adequate. 
The true evolution of wave 1 is faithfully retrieved (Fig. 6). Contamination 
from spurious high frequencies, evident at the beginning and end of the 
original retrieval (Fig. 4), is virtually absent when the sample is made 
cyclic. (Fig./7). 
I| os Sl 
04 S 
0.3 
a 7 | | A 
-40 -30 -20 -10 O 10 20 30 40 
t 
Fig. 6 As for Fig. 5 but for observations over the time interval [-2.0, 2.0], 
extended by a cosine taper to zero on the initial and final days. Time 
evolution te now oyclic. As a result the correct evolution is eynoptically 
recovered over the entire observation interval. 
  
  
  
  
  
  
  
151