Tracking Behaviour of Lattice Filters for Linear and Quadratic FM Signals

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Tracking Behaviour of Lattice Filters for Linear and Quadratic FM Signals

Show simple item record Kahaei, M.H. Zoubir, A.M. Boashash, B Deriche, M 2012-06-17T16:23:00Z 2012-06-17T16:23:00Z 1997
dc.identifier.citation Digital Signal Processing for Communication Systems, T. Wysocki, editor, pp. 207-214, Kluwer Academic Publishers, 1997 en_US
dc.description.abstract In practical applications, the statistics of the signal are unknown and time-varying. Hence, the coefficients of an adaptive filter converge towards the optimal values and track the time-varying statistics of the input signal during the steady state time. In order to analyse the performance of adaptive filters. the behaviour of optimal and adaptive coefficients as well as the resulting output error signals need to be carefully studied. Frequency modulated (FM) input signals in noise are a well-known class of non stationary random processes with time-varying spectra. They possess a structure which facilitates the theoretical analysis and are also encountered in many real applications. In investigating the behaviour of adaptive filters tracking linear FM signals, a great effort has been devoted to transversal filters [9), [I). However, an alternative structure is the lattice filter with its attractive properties. Some of these properties include high convergence speed, easy computations, less sensitivity to eigenvalues spread, ease of implementations, and providing a Gram-Schmidt type of orthogonalisation of the input signal [8). The intent of this paper is to investigate new properties of FIR lattice filters in presence of quadratic and linear FM signals [10). It will theoretically be shown that the reflection coefficients for such signals produce linear FM and sinusoidal signals. respectively_ We have called this property as the polynomial order reducing (POR) property of the lattice filter. Additionally, the relationship between the forward and backward error signals (residuals) with the filter order and the input signal to noise ratio is presented. To illustrate the tracking behaviour of the adaptive fi Iter, in the first experiment, the instantaneous frequency (IF) [2] of a quadratic FM signal is estimated under the assumption that the input signal has an AR structure. To update the adaptive coefficients, the unnormalised stochastic gradient (SG) algorithm is applied. While other on-line IF estimation techniques such as zero-crossing and central finite difference (CFO) methods produce a high variance even al high SNRs [3), adaptive FIR lattice filters perform very well, even at low SNRs. In the second experiment, a new technique is presented based on the POR property to estimate the IF of a linear FM signal. The results compared to those of the adaptive line enhancer (ALE) [51 show a lower mean-square error (MSE) and bias in the IF estimates. en_US
dc.language.iso en en_US
dc.publisher Kluwer Academic Publishers en_US
dc.title Tracking Behaviour of Lattice Filters for Linear and Quadratic FM Signals en_US
dc.type Book chapter en_US

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