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Instantaneous Frequency Estimation Based On Time-Varying Auto Regressive Model And WAX-Kailath Algorithm
G Ravi Shankar Reddy, Dr Rameshwar Rao
Pages - 43 - 66 | Revised - 10-08-2014 | Published - 15-09-2014
Published in Signal Processing: An International Journal (SPIJ)
MORE INFORMATION
KEYWORDS
Basis Functions, Instantaneous Frequency Estimation, Maximum Likelihood Estimation, Time-Varying Autoregressive Model, Wax-kailath Algorithm.
ABSTRACT
Time-varying autoregressive (TVAR) model is used for modeling non stationary signals, Instantaneous frequency (IF) and time-varying power spectral density are then extracted from the TVAR parameters. TVAR based Instantaneous frequency (IF) estimation has been shown to perform very well in realistic scenario when IF variation is quick, non-linear and has short data record. In TVAR modeling approach, the time-varying parameters are expanded as linear combinations of a set of basis functions .In this article, time poly nominal is chosen as basis function. Non stationary signal IF is estimated by calculating the angles of the roots (poles) of the time-varying autoregressive polynomial at every sample instant. We propose modified covariance method that utilizes both the time varying forward and backward linear predictors for estimating the time-varying parameters and then IF estimate. It is shown that performance of proposed modified covariance method is superior than existing covariance method which uses only forward linear predictor for estimating the time-varying parameters. The IF evaluation based on TVAR modeling requires efficient estimation of the time-varying coefficients by solving a set of linear equations referred as the general covariance equations. When covariance matrix is of high order, usual approach such as Gaussian elimination or direct matrix inversion is computationally incompetent for solving such a structure of equations. We apply recursive algorithm to competently invert the covariance matrix, by means of Wax-Kailath algorithm which exploits the block-Toeplitz arrangement of the covariance matrix for its recursive inversion, which is the central part of this article. The order determination of TVAR model is addressed by means of the maximum likelihood estimation (MLE) algorithm.
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Mr. G Ravi Shankar Reddy
CVR College of Engineering - India
ravigosula_ece39@yahoo.co.in
Mr. Dr Rameshwar Rao
JNTUH - India