Kw. Martin et M. Padmanabhan, USING AN IIR ADAPTIVE FILTER BANK TO ANALYZE SHORT DATA SEGMENTS OF NOISY SINUSOIDS, IEEE transactions on signal processing, 41(8), 1993, pp. 2583-2590
The spectral analysis of short data segments has traditionally been do
ne using eigenvalue-based matrix-analysis methods. Recently, some IIR
adaptive filters have been used for the spectral analysis of multisinu
soidal signals corrupted by noise, but these have only been used for a
nalyzing long data segments, since they normally require the analysis
of many data samples before they converge. They do have the advantages
of being easy to program, do not require much memory for storage, and
sometimes have few divisions. In addition, they often have very good
resolution, especially for characterizing sinusoids at frequencies muc
h less than the sampling frequency. A new IIR adaptive resonator-in-a-
loop filter bank is described that can be used for high-resolution spe
ctral analysis of not only long data segments, but short data segments
as well, with accuracies approaching the Cramer-Rao lower bounds for
SNR's as small as 10 dB. The basic approach taken is to reanalyze the
data segment many times while running the data forwards and backwards
through the filter, as the coefficients converge. Special care is take
n at the data endpoints, when reinitializing the filter state variable
s, to eliminate transients.