Use of Window Functions and Kalman Filtering in Spectral Estimation

摘要

The periodogram, the square of the magnitude of the Fourier Transform, is widelyused to estimate the spectral content of sampled processes. The performance of the periodogram is degraded by spectral leakage. This is the consequence of processing finite-length data records. Classical means of enhancing periodogram performance are the use of tapered window functions and averaging of several periodograms. These methods smooth the spectral estimate, but at a loss of resolution. A non-stationary Kalman filter was applied to the periodogram of untapered (i.e., rectangular windowed) time data in an effort smooth the noise portions of the periodogram while leaving the main spectral response unaltered. The Kalman filter was able to enhance the periodogram. Best results were obtained in the single spectral peak case. Even in the case of multiple spectral peaks, the resolution of the unfiltered periodogram was largely preserved since the filtering algorithm was designed to selectively smooth the noise-only segments of the spectral estimate. Keywords: Theses. (Author) (kr)