Spectrum estimation using adaptive filters

Abstract

In this work, the adaptive discrete-time, linear nonrecursive filters (or estimators) designed by the Least Mean Square (LMS) algorithm are investigated. The developmeni of adaptive techniques for estimating the parameters of sinusoidal signais in white noise is important in many applications. Therefore, a signal enhancing technique for statistically stationary signals based on conventional Least Mean Square (LMS) adaptive filtering and some other newly developed procedures of adaptive spectral estimation of discrete time series arepresented in this thesis. An adaptiye filter configuration known as the Adaptive Line Enhancer (ALE) originally suggested by Widrow [1] for the detection of sinusoidal signals in wide band noise is studied in detail. New expressions related to the decorrelation parameter for the cases of one, two and multiple sinusoids are obtained. This thesis also investigates the method in [10] for eliminating sinusoidal or other periodic interference corrupting a signal. This task is typically accomplished by explicitly measuring the frequency of the interference and implementing a notch filter at that frequency. For the colored noise case, the optimal filter length for ALE is obtained by maximizing the SNR ratio of ALE. The + estimation in LMS algorithm will be better if the estimates of the tap gain coefficients are better. Better estimates are obtained by running the LMS algorithm longer. Therefore, it is useful to have a rapidly convergent algorithm and so called Ladder or Lattice filter. For that reason we introduce the Lattice Filter Implementation of the general ALE as in [36]. Also a class of stable and efficient recursive lattice methods for linear prediction depending on the choosen reflection coefficients. Computer simulations are also performed to discuss everything in the thesis.