Using an IIR Adaptive Filter Bank to Analyze Short Data Segments of Noisy Sinusoids

Abstract

The spectral analysis of short data segments has traditionally been done using eigenvalue-based matrix-analysis methods. Recently, some IIR adaptive filters have been used for the spectral analysis of multisinusoidal signals corrupted by noise, but these have only been used for analyzing 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 much less than the sampling frequency. A new IIR adaptive resonator-in-a-loop filter bank is described that can be used for high-resolution spectral 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 taken at the data endpoints, when reinitializing the filter state variables, to eliminate transients. © 1993 IEEE