Spelling suggestions: "subject:"block toeplitz"" "subject:"block teplitz""
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Structure of Toeplitz-composition operatorsSyu, Meng-Syun 14 February 2011 (has links)
Let $vp$ be a $L^infty$ function on the unit circle $Bbb T$ and
$ au$ be an elliptic automorphism on the unit disc $Bbb D$. In this paper, we will show that $T_vp C_ au$, i.e., the product of the Toeplitz operator $T_vp$ and the composition operator $C_ au$ on $H^2$, is similar to a block Toeplitz matrix if $ au$ has finite
order.
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Implementation of Instantaneous Frequency Estimation based on Time-Varying AR ModelingKadanna Pally, Roshin 27 May 2009 (has links)
Instantaneous Frequency (IF) estimation based on time-varying autoregressive (TVAR) modeling has been shown to perform well in practical scenarios when the IF variation is rapid and/or non-linear and only short data records are available for modeling. A challenging aspect of implementing IF estimation based on TVAR modeling is the efficient computation of the time-varying coefficients by solving a set of linear equations referred to as the generalized covariance equations. Conventional approaches such as Gaussian elimination or direct matrix inversion are computationally inefficient for solving such a system of equations especially when the covariance matrix has a high order.
We implement two recursive algorithms for efficiently inverting the covariance matrix. First, we implement the Akaike algorithm which exploits the block-Toeplitz structure of the covariance matrix for its recursive inversion. In the second approach, we implement the Wax-Kailath algorithm that achieves a factor of 2 reduction over the Akaike algorithm in the number of recursions involved and the computational effort required to form the inverse matrix.
Although a TVAR model works well for IF estimation of frequency modulated (FM) components in white noise, when the model is applied to a signal containing a finitely correlated signal in addition to the white noise, estimation performance degrades; especially when the correlated signal is not weak relative to the FM components. We propose a decorrelating TVAR (DTVAR) model based IF estimation and a DTVAR model based linear prediction error filter for FM interference rejection in a finitely correlated environment. Simulations show notable performance gains for a DTVAR model over the TVAR model for moderate to high SIRs. / Master of Science
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