Block implementation on lattice prefiltering structure
Student thesis: Master's Thesis
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Award date  14 Dec 1998 
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Permanent Link  https://scholars.cityu.edu.hk/en/theses/theses(827c46d2b1bd4a9c98291ec64a158f75).html 

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Abstract
A new prefiltering structure is developed which is called the lattice prefiltering structure. The structure consists of two parts. The first part is a lattice predictor of order P functioning as prefilter. The second part is a bank of subfilters using backward prediction errors of zeroth order to Pth order generated by the lattice predictor. Unlike other linear prediction prefilter, it is not a cascade structure. It forms a class of filters that can provide the minimum mean square error same as the Wiener solution and realize general transversal transfer function. If the prefilter order P equals the transversal filter length, the structure will become the conventional lattice filtering structure. The function of the prefilter is to preequalize the input signal in order to reduce the eigenvalue spread. Lattice filter is chosen for prefilter because it has the advantage of the decoupling properties between successive stages. An optimum lattice prefiltering structure is defined and it is shown to provide fast convergence rate. GAL and LMS are respectively used for the adaptation of the lattice prefilter and the main filter for their simplicities. Block digital filtering is applied to both the lattice prefilter and the main filter in order to reduce computational complexity. The reflection coefficients of the lattice prefilter are updated according to leastsquare criteria which can be reduced to the Burg algorithm. BLMS is applied to reduce the computational complexity of the main filter. Optimum step size BLMS (OSSBLMS) algorithm is presented for step size optimization which has significant improvement of the convergence rate over the BLMS algorithm. The steady state mean square error can also be improved by using a larger block length. By using the BLS criteria, a recursive formula is formed to calculate the optimum step size and hence it results in a reduction of computational complexity. By making use of the block processing idea, computational complexity is reduced by eliminating the redundant calculation of the convolution process. Longlength, which is regarded as long filter length and large block size, problem can be iterated by efficient short algorithms. In some cases, the complexity is even lower than FFT. Further simplification of OSSBLMS is introduced in which the error terms are approximated. The lattice prefilter can also be implemented efficiently by rewriting the formulae of the GAL in block lattice algorithms. Applying both OSSBLMS and block lattice algorithms on the lattice prefiltering structure, the convergence rate can be improved considerably.
 Lattice theory, Digital filters (Mathematics)