Conclusions and Software - Spectral Analysis of Signals: The Missing Data Case - page 88

CHAPTER 7

Conclusions and Software

7.1 CONCLUDING REMARKS
We have presented some recent results on nonparametric spectral analysis with
missing samples. In particular, we have provided detailed discussions on using
GAPES for the gapped-data and the more general MAPES for the arbitrarily
missed-data spectral estimation problems. Both 1-D and 2-D applications are
considered.
Among these incomplete-data algorithms, GAPES has the least computa-
tional complexity, while MAPES-EM tends to give the best performance. Ac-
cording to their computational complexities, these algorithms can be arranged in
ascending order, starting from the most efficient one: GAPES, MAPES-CM,
MAPES-EM2, and MAPES-EM1. Clearly, there is a tradeoff between spectral
estimation performance and computational efficiency.
The reader needs to find out which algorithm is the best choice for each par-
ticular application, in terms of estimation accuracy and computational complexity.
We now provide some general guidelines based on our own experience:

1. If the missing samples are grouped together and large continuous data seg-

ments are available, GAPES is recommended due to its good performance
for the gapped-data problem and low computational complexity.

2. If the missing samples occur in arbitrary patterns, the MAPES algo-

rithms should be used due to their excellent performances. MAPES-
CM is faster than MAPES-EM1 and MAPES-EM2, but with slightly