A floating point error analysis of the Recursive Least Squares and Least Mean Squares (LMS) algorithms is presented. Both the prewindowed growing memory RLS algorithm (λ=1) for stationary systems and the exponential ...
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A floating point error analysis of the Recursive Least Squares and Least Mean Squares (LMS) algorithms is presented. Both the prewindowed growing memory RLS algorithm (λ=1) for stationary systems and the exponential sliding window RLS algorithm (λ < 1) for time varying systems are studied. For both algorithms the expression for the mean square prediction error and the expected value of the weight error vector norm are derived in terms of the variance of the floating point noise sources. The results point to a trade off in the choice of the forgetting factor, λ. In order to reduce the effects of additive noise and the floating point noise due to the inner product calculation of the desired signal, λ must be chosen close to one. On the other hand, the floating point noise due to floating point addition in the weight vector update recursion increases as \lambda\rightarrow1 . Floating point errors in the calculation of the weight vector correction term, however, do not effect the steady state error and have a transient effect. Similar results are obtained for the LMS algorithm where a tradeoff exists in the choice of the loop gain.
The Fast Pole-Zero (ARMA) Recursive Least Squares Algorithm is derived using geometric projections. The new algorithm has a reduced number of computations compared to the pole-zero fast Kalman algorithm. In particular...
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The Fast Pole-Zero (ARMA) Recursive Least Squares Algorithm is derived using geometric projections. The new algorithm has a reduced number of computations compared to the pole-zero fast Kalman algorithm. In particular, four vector inner products and scalar-times-vector operations are eliminated. This is particularly important in multiprocessor implementations of the algorithm. The geometric approach provides insight and useful interpretations of the various filters and residuals that form the algorithm. Simulations verifying the performance of the algorithm are presented where the poles and zeroes of an IIR filter are estimated.
This paper examines the derivation of a general order, multiple input version of the fast transversal recursive least squares filter algorithm. The new algorithm, in which the order (or number of taps) associated with...
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This paper examines the derivation of a general order, multiple input version of the fast transversal recursive least squares filter algorithm. The new algorithm, in which the order (or number of taps) associated with each input channel is independent, is distinguished from the previously published multichannel form of the fast transversal RLS algorithm, wherein each input channel was con strained to have the same order. This additional flexibility allows assignment of filter resources to particular channels, or independent assignment to the pole/zero estimators in an ARMA system identification application. A summary of the new algorithm is given, in proper order of execution. An operations count is also provided for each equation
Electronics storage systems, image display stations, protocols, and networks capable of managing a large amount of data must be developed in order for picture archival and communications systems to become a reality, T...
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Adaptive least mean square (LMS) filters are shown to be effective in reducing harmonic noise on distribution power lines. The efficiency of these filters can be improved by imposing constraints.
Adaptive least mean square (LMS) filters are shown to be effective in reducing harmonic noise on distribution power lines. The efficiency of these filters can be improved by imposing constraints.
This paper provides an analytical derivation of a simple noniterative technique for extracting a multiple impulse excitation model for synthesized speech directly from the LPC residual sequence. While suboptimal with ...
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This paper provides an analytical derivation of a simple noniterative technique for extracting a multiple impulse excitation model for synthesized speech directly from the LPC residual sequence. While suboptimal with respect to "multipulse" techniques, this method is very applicable for speech enhancement where processor capability is limited. The results suggest an additional "orthogonality" requirement between the excitation sequence and the resulting prediction error, which aids in the intuitive understanding of the method.
In this paper, the adaptive Least Mean Squares (LMS) algorithm is used to separate speaker-produced "information" from interferer-produced "noise" on the basis of the difference in power levels ass...
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In this paper, the adaptive Least Mean Squares (LMS) algorithm is used to separate speaker-produced "information" from interferer-produced "noise" on the basis of the difference in power levels associated with the two phenomena. This method exploits the property of LMS that it rapidly adapts for the dominant excitation modes while simultaneously adapting very slowly for the weaker modes of excitation. This selective convergence property of LMS is next analyzed using an eigenvalue-eigenvector approach which easily displays the signal separation property. Lastly, computer simulations are presented which verify the analysis above for representative synthetic speech waveforms.
Concurrent process structured software can be used as a tool for studying the behavior of parallel digital signalprocessing systems. By modeling alternative architectures for a given application and characterizing th...
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Concurrent process structured software can be used as a tool for studying the behavior of parallel digital signalprocessing systems. By modeling alternative architectures for a given application and characterizing the interactions of concurrent processes, an evaluation of relative efficiencies can be made. Presented here are models of three architectures for time domain harmonic scaling (TDHS) of speech. Their implementations and the software tools required to study their behavior are described.
This paper addresses various aspects of motion-compensated interframe coding. The image sequence data is investigated in an attempt to develop a more thorough analysis of the convergence requirements and the convergen...
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This paper addresses various aspects of motion-compensated interframe coding. The image sequence data is investigated in an attempt to develop a more thorough analysis of the convergence requirements and the convergence rate. A new motion prediction technique is used which increases the validity of the assumptions made in proving convergence and which decreases the total prediction error. Simulation results are presented to indicate the improvement of the proposed motion prediction scheme and to indicate the results of the convergence analysis.
In image coding, image information can often be transmitted with relatively little bandwidth requirement. This is the case in the pixel domain if there are large blocks of homogeneous intensity within a single frame, ...
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In image coding, image information can often be transmitted with relatively little bandwidth requirement. This is the case in the pixel domain if there are large blocks of homogeneous intensity within a single frame, or when comparing adjacent frames there are large blocks of unchanged pixels. In the frequency domain, this is the case when only a few of the frequency coefficients are deemed significant. This paper presents an algorithm for improving the bandwidth compression of the error pattern generated by typical motion-compensated coding techniques. The algorithm involves two well established techniques; conventional transform coding and the method of successive Projection onto Convex Sets.
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