APES for Complete Data Spectral Estimation - Spectral Analysis of Signals: The Missing Data Case - page 6

CHAPTER 2

APES for Complete Data
Spectral Estimation

2.1 INTRODUCTION
Filter-bank approaches are commonly used for spectral analysis. As nonparametric
spectral estimators, they attempt to compute the spectral content of a signal with-
out using any apriori model information or making any explicit model assumption
about the signal. For any of these approaches, the key element is to design narrow-
band filters centered at the frequencies of interest. In fact, the well-known peri-
odogram can be interpreted as such a spectral estimator with a data-independent
filter-bank. In general, data-dependent (or data-adaptive) filters outperform their
data-independent counterparts and are hence preferred in many applications. A
well-known adaptive filter-bank method is the Capon spectral estimator [12]. More
recently, Li and Stoica [13] devised another adaptive filter-bank method with en-
hanced performance, which is referred to as the amplitude and phase estimation
(APES). APES surpasses its rivals in several aspects [15, 25] and find applications
in various fields [1, 26-31].
In this chapter, we derive the APES filter from pure narrowband-filter de-
sign considerations [32]. It is useful as the initialization step of the algorithms in
Chapter 3. The remainder of this chapter is organized as follows: The problem
formulation is given in Section 2.2 and the forward-only APES filter is presented
in Section 2.3. Section 2.4 provides a two-step filtering interpretation of the APES
estimator. Section 2.5 shows how the forward-backward averaging can be used