Introduction - Spectral Analysis of Signals: The Missing Data Case - page 3

tasks because of their robustness and high computational efficiency. However, they
suffer from low resolution and poor accuracy problems. Many advanced spectral
estimation methods have also been proposed, including parametric [9-11] and
nonparametric adaptive filtering based approaches [12, 13]. One problem associated
with the parametric methods is order selection. Even with properly selected order, it
is hard to compare parametric and nonparametric approaches since the parametric
methods (except [11]) do not provide complex amplitude estimation. In general,
the nonparametric approaches are less sensitive to data mismodelling than their
parametric counterparts. Moreover, the adaptive filter-bank based nonparametric
spectral estimators can provide high resolution, low sidelobes, and accurate spectral
estimates while retaining the robust nature of the nonparametric methods [14, 15].
These include the amplitude and phase estimation (APES) method [13] and the
Capon spectral estimator [12].
However, the complete-data spectral estimation methods do not work well
in the missing-data case when the missing data samples are simply set to zero. For
the DFT-based spectral estimators, setting the missing samples to zero corresponds
to multiplying the original data with a windowing function that assumes a value of
one whenever a sample is available, and zero otherwise. In the frequency domain,
the resulting spectrum is the convolution between the Fourier transform of the
complete data and that of the windowing function. Since the Fourier transform of
the windowing function typically has an underestimated mainlobe and an extended
pattern of undesirable sidelobes, the resulting spectrum will be poorly estimated and
contain severe artifacts. For the parametric and adaptive filtering based approaches,
similar performance degradations will also occur.
1.2 MISSING-DATA CASE
For missing-data spectral estimation, various techniques have been developed pre-
viously. In [16] and [17], the Lomb-Scargle periodogram is developed for irregu-
larly sampled (unevenly spaced) data. In the missing-data case, the Lomb-Scargle