Adaptive Windows via Kalman Filtering in the Spectral Domain

摘要

Application of classical windows to time series data is a means of enhancing theperformance of the periodogram. Use of these classical windows results in the broadening of the spectral mainlobe. A Kalman filter will smooth spectral data by dividing the periodogram of unwindowed time series data into piecewise constant segments, ideally into noise only signal only segments. This allows for a more accurate representation of the mainlobe of the original periodogram. The Kalman filter was modified to alter the filter parameter (beta) during filtering to provide maximum smoothing during the noise-only portion of the periodogram while leaving the main spectral peak essentially unaltered. A second modification was made to substitute the original raw values of the periodogram for the filter estimates during detected up-transitions while smoothing the noise-only segments in the same manner as in the original Kalman algorithm. This further enhances the preservation of the mainlobe of the periodogram and lowers the noise floor 1 to 3 dB over that of the original Kalman filter. These processes were further enhanced by stacking the output periodograms and displaying them as LOFAR output on the Sun workstation. NCAR graphics grey-toning is used to generate the LOFAR displays.