@misc{townsend_punjabi_duel-hallen_alexander_1996, title={Apparatus and method for echo characterization of a communication channel}, volume={5,577,116}, number={1996 Nov. 19}, publisher={Washington, DC: U.S. Patent and Trademark Office}, author={Townsend, K. and Punjabi, H. and Duel-Hallen, A. and Alexander, S. T.}, year={1996} }
 @article{alexander_ghirnikar_1993, title={A METHOD FOR RECURSIVE LEAST-SQUARES FILTERING BASED UPON AN INVERSE QR DECOMPOSITION}, volume={41}, ISSN={["1053-587X"]}, DOI={10.1109/tsp.1993.193124}, abstractNote={A new computationally efficient algorithm for re- cursive least squares filtering is derived, which is based upon an inverse QR decomposition. The method solves directly for the time-recursive least squares filter vector, while avoiding the highly serial backsubstitution step required in previously de- rived direct QR approaches. Furthermore, the method employs orthogonal rotation operations to recursively update the filter, and thus preserves the inherent stability properties of QR ap- proaches to recursive least squares filtering. The results of sim- ulations over extremely long data sets are also presented, which suggest stability of the new time-recursive algorithm. Finally, parallel implementation of the resulting method is briefly dis- cussed, and computational wavefronts are displayed.}, number={1}, journal={IEEE TRANSACTIONS ON SIGNAL PROCESSING}, author={ALEXANDER, ST and GHIRNIKAR, AL}, year={1993}, month={Jan}, pages={20–30} }
 @inproceedings{alexander_stonick_1993, title={Fast adaptive polynomial root tracking using a homotopy continuation method}, DOI={10.1109/icassp.1993.319539}, abstractNote={A fast adaptive method for tracking the roots of a time-varying complex domain polynomial is derived. The approach uses the method of homotopy continuation and is efficient from both mathematical and implementation standpoints. The method is globally convergent and tracks all roots simultaneously. An example that verifies the accurate tracking ability of the algorithm is presented. Applications which could benefit from this method are also discussed.<<ETX>>}, booktitle={1993 IEEE International Conference on Acoustics, Speech, and Signal Processing}, author={Alexander, S. T. and Stonick, V. L.}, year={1993} }
 @article{ghirnikar_alexander_plemmons_1992, title={A PARALLEL IMPLEMENTATION OF THE INVERSE QR ADAPTIVE FILTER}, volume={18}, ISSN={["0045-7906"]}, DOI={10.1016/0045-7906(92)90021-5}, abstractNote={A systolic array architecture is proposed for an inverse QR algorithm for recursive least squares signal processing. This algorithm provides a solution for the least squares filter vector which does not require the computationally intensive step of backsubstitution needed in the direct QR method. The inverse QR algorithm is therefore highly amenable to a parallel implementation, resulting in a structure which produces the N filter coefficients every N + 1 clock cycles. Within the paper, the individual processing elements contained in the inverse QR algorithm are outlined, after which it is demonstrated how these processing elements may be connected to implement the overall inverse QR array. Timing considerations, data rates, latency and throughput are also discussed.}, number={3-4}, journal={COMPUTERS & ELECTRICAL ENGINEERING}, author={GHIRNIKAR, AL and ALEXANDER, ST and PLEMMONS, RJ}, year={1992}, pages={291–300} }
 @article{stonick_alexander_1992, title={GLOBALLY OPTIMAL RATIONAL APPROXIMATION USING HOMOTOPY CONTINUATION METHODS}, volume={40}, ISSN={["1053-587X"]}, DOI={10.1109/78.157240}, abstractNote={Homotopy continuation methods are applied to the nonlinear problem of approximating a higher-order system by a lower-order rational model, such that the mean-square modeling error is minimized. A homotopy function is constructed which creates distinct paths from each of the known solutions of a simple problem to each of the solutions of the desired nonlinear problem. This homotopy function guarantees that the globally optimum rational approximation solution may be determined by finding all the solutions. A simple numerical continuation algorithm is described for following the paths to the optimum solution. A numerical example is included which demonstrates that the globally optimum model will be obtained by applying this homotopy continuation method. >}, number={9}, journal={IEEE TRANSACTIONS ON SIGNAL PROCESSING}, author={STONICK, VL and ALEXANDER, ST}, year={1992}, month={Sep}, pages={2358–2361} }
 @article{bottomley_alexander_1991, title={A NOVEL-APPROACH FOR STABILIZING RECURSIVE LEAST-SQUARES FILTERS}, volume={39}, ISSN={["1053-587X"]}, DOI={10.1109/78.91147}, abstractNote={A novel approach for stabilizing recursive least squares (RLS) filters is presented. The approach relies on a detailed fixed point analysis, which provides two important benefits. The analysis reveals a bias in the error propagation mechanism, providing an analytical basis for instability problems. The analysis then indicates which specific roundoff errors are causing instability. These roundoff errors are then biased in such a way that the overall filter is biased towards stable performance. Experimental results indicate that stability can be achieved with negligible loss in least squares performance. >}, number={8}, journal={IEEE TRANSACTIONS ON SIGNAL PROCESSING}, author={BOTTOMLEY, GE and ALEXANDER, ST}, year={1991}, month={Aug}, pages={1770–1779} }
 @misc{stonick_alexander_1991, title={A RELATIONSHIP BETWEEN THE RECURSIVE LEAST-SQUARES UPDATE AND HOMOTOPY CONTINUATION METHODS}, volume={39}, ISSN={["1053-587X"]}, DOI={10.1109/78.80849}, abstractNote={The authors present an alternative derivation of the general recursive least squares (RLS) algorithm using homotopy approaches. Homotopy continuation methods are briefly described, and a simple iterative update for path following is derived. A homotopy function is then constructed using the RLS filtering criteria. The equivalence between the iterative update for following the path defined by this homotopy function and the general RLS update is derived. Finally, an intuitive explanation of this result is presented. >}, number={2}, journal={IEEE TRANSACTIONS ON SIGNAL PROCESSING}, author={STONICK, VL and ALEXANDER, ST}, year={1991}, month={Feb}, pages={530–532} }
 @article{hubing_alexander_1991, title={STATISTICAL-ANALYSIS OF INITIALIZATION METHODS FOR RLS ADAPTIVE FILTERS}, volume={39}, ISSN={["1941-0476"]}, DOI={10.1109/78.91150}, abstractNote={Theoretical analysis is used to evaluate the mean and second-moment properties of recursive least squares algorithms incorporating the fast exact initialization and soft constrained initialization methods during the initialization period. It is shown that the weight vector mean and covariance produced by fast exact initialization are undefined for this period. Theoretical results are derived for soft constrained initialization that show that the weight vector mean and covariance are finite, and expressions are given for these quantities. Simulations for various cases are presented to support the accuracy of these theoretical results. >}, number={8}, journal={IEEE TRANSACTIONS ON SIGNAL PROCESSING}, author={HUBING, NE and ALEXANDER, ST}, year={1991}, month={Aug}, pages={1793–1804} }
 @misc{hubing_alexander_1990, title={INVERSE INVARIANT DISTRIBUTIONS}, volume={38}, ISSN={["0096-3518"]}, DOI={10.1109/29.56069}, abstractNote={The probability density function associated with a random variable Z is inverse-invariant if it is identical to the density function associated with the inverse of Z. An intuitive method of finding inverse-invariant density functions is presented, with examples and notes on where these distributions arise. Specific parameter estimation algorithms which produce estimates having inverse-invariant distributions are discussed. >}, number={6}, journal={IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING}, author={HUBING, NE and ALEXANDER, ST}, year={1990}, month={Jun}, pages={1059–1061} }
 @article{alexander_pan_plemmons_1988, title={ANALYSIS OF A RECURSIVE LEAST-SQUARES HYPERBOLIC ROTATION ALGORITHM FOR SIGNAL-PROCESSING}, volume={98}, ISSN={["0024-3795"]}, DOI={10.1016/0024-3795(88)90158-9}, abstractNote={The application of hyperbolic plane rotations to the least squares downdating problem arising in windowed recursive least squares signal processing is studied. A forward error analysis is given to show that this algorithm can be expected to perform well in the presence of rounding errors, provided that the problem is not too ill conditioned. The hyperbolic rotation algorithm is shown to be forward (weakly) stable and, in fact, comparable to an orthogonal downdating method shown to be backward stable by Stewart. It is shown in detail how the method's accuracy depends upon the conditioning. Numerical comparisons are made with the usual method based upon orthogonal rotations as implemented in LINPACK. Both methods have the important advantage over the classical normal equations appraoch that they can be effectively implemented on special purpose signal processing devices requiring shorter word-lengths. However, the hyperbolic rotation requires n2 fewer multiplications and additions for each downdating step than the orthogonal method, where n is the number of least squares filter coefficients. In addition, it is more amenable to implementation on a variety of vector and parallel machines. In many signal processing applications n is not large, and if n processors are available, then the downdating process can be accomplished in 2n time steps by the hyperbolic rotation method.}, journal={LINEAR ALGEBRA AND ITS APPLICATIONS}, author={ALEXANDER, ST and PAN, CT and PLEMMONS, RJ}, year={1988}, month={Jan}, pages={3–40} }
 @article{alexander_ardalan_1987, title={Analytical finite precision results for Burg?s algorithm and the autocorrelation method of linear prediction}, volume={35}, journal={IEEE Transactions on Acoustics, Speech, and Signal Processing}, author={Alexander, S. T. and Ardalan, S. H.}, year={1987}, pages={626–635} }
 @misc{ardalan_alexander_1987, title={Echo canceller using parametric methods}, volume={4,677,668}, number={1987 Jun. 30}, publisher={Washington, DC: U.S. Patent and Trademark Office}, author={Ardalan, S. H. and Alexander, S. T.}, year={1987} }
 @article{ardalan_alexander_1987, title={FIXED-POINT ROUNDOFF ERROR ANALYSIS OF THE EXPONENTIALLY WINDOWED RLS ALGORITHM FOR TIME-VARYING SYSTEMS}, volume={35}, ISSN={["0096-3518"]}, DOI={10.1109/tassp.1987.1165207}, abstractNote={A fixed-point roundoff error analysis of the exponentially windowed RLS algorithm is presented. It is shown that a tradeoff exists in the choice of the forgetting factor λ. In order to reduce the sensitivity of the algorithm to additive noise, λ must be chosen close to one. On the other hand, the roundoff error increases as \lambda \rightarrow 1 . It is shown that the algorithm is stabilized with λ \lambda \rightarrow 1 . To derive the theoretical results, it is assumed that the input signal is a white Gaussian random process. Finally, simulations are presented which confirm the theoretical findings of the paper.}, number={6}, journal={IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING}, author={ARDALAN, SH and ALEXANDER, ST}, year={1987}, month={Jun}, pages={770–783} }
 @article{alexander_1987, title={TRANSIENT WEIGHT MISADJUSTMENT PROPERTIES FOR THE FINITE PRECISION LMS ALGORITHM}, volume={35}, ISSN={["0096-3518"]}, DOI={10.1109/tassp.1987.1165279}, abstractNote={Implementation of the least mean squares (LMS) algo- rithm in finite precision (FP) arithmetic introduces degradations in performance compared to the infinite precision (IP) implementation. This paper derives a new and more accurate analytical result for the expected misadjustment in the LMS weight vector due to FP effects. Whereas previous results have been applicable only during steady state, the results of this present paper are applicable to both the transient adaptation period and steady state. Experimental data are then pre- sented which show the new analytical results to be valid for approxi- mating the weight misadjustment during the transient adaptation pe- riod over a wide range of filter and data values.}, number={9}, journal={IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING}, author={ALEXANDER, ST}, year={1987}, month={Sep}, pages={1250–1258} }
 @article{miller_alexander_faber_1986, title={AN SIMD MULTIPROCESSOR RING ARCHITECTURE FOR THE LMS ADAPTIVE ALGORITHM}, volume={34}, ISSN={["0090-6778"]}, DOI={10.1109/tcom.1986.1096423}, abstractNote={A new architecture for a single instruction stream, multiple data stream (SIMD) implementation of the LMS adaptive algorithm is investigated. This is denoted as a ring architecture, due to its physical configuration, and it effectively solves the latency problem often associated with prediction error feedback in adaptive filters. The multiprocessor ring efficiently updates the filter input vector by operating as a pipeline structure, while behaving as a parallel structure in computing the filter output and applying the weight adaptation algorithm. Last, individual processor timing and capacity considerations are examined.}, number={1}, journal={IEEE TRANSACTIONS ON COMMUNICATIONS}, author={MILLER, TK and ALEXANDER, ST and FABER, LJ}, year={1986}, month={Jan}, pages={89–92} }
 @book{alexander_1986, title={Adaptive signal processing: Theory and applications}, ISBN={0387963804}, DOI={10.1007/978-1-4612-4978-8}, publisher={New York: Springer-Verlag}, author={Alexander, S. T.}, year={1986} }
 @article{alexander_1986, title={Fast adaptive filters: A geometrical approach}, DOI={10.1109/massp.1986.1165385}, abstractNote={This is a tutorial article on the application of geometrical vector space concepts for deriving the rapidly converging, reduced computation structures known as fast recursive least squares (RLS) adaptive filters. Since potential applications of fast RLS, such as speech coding [1] and echo, cancellation [2], have been previously examined in the ASSP Magazine, this article focuses instead on an intuitive geometrical approach to deriving these fast RLS filters for linear prediction. One purpose of this article is to keep the required mathematics at a minimum and instead highlight the properties of the fast RLS filters through geometrical interpretation. The geometrical vector space concepts in this article are then applied to deriving the very important fast RLS structure known as the fast transversal filter (FTF).}, journal={IEEE Transactions on Acoustics, Speech, and Signal Processing}, author={Alexander, S. T.}, year={1986}, pages={18–28} }
 @misc{alexander_1985, title={A SIMPLE NONITERATIVE SPEECH EXCITATION ALGORITHM USING THE LPC RESIDUAL}, volume={33}, ISSN={["0096-3518"]}, DOI={10.1109/tassp.1985.1164568}, abstractNote={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.}, number={2}, journal={IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING}, author={ALEXANDER, ST}, year={1985}, pages={432–434} }
 @inbook{alexander_rajala_1985, title={Adaptive Compression of Teleconference Sequences Using the LMS Algorithm}, ISBN={9780442278267}, booktitle={Teleconferencing}, publisher={New York: Van Rostrand Reinhold, Inc.}, author={Alexander, S.T. and Rajala, S.A.}, editor={Ramamohan Rao and Srinivasan, RamEditors}, year={1985} }
 @misc{alexander_rajala_1985, title={IMAGE COMPRESSION RESULTS USING THE LMS ADAPTIVE ALGORITHM}, volume={33}, ISSN={["0096-3518"]}, DOI={10.1109/tassp.1985.1164595}, abstractNote={The LMS algorithm may be used to adapt the coefficients of an adaptive prediction filter for image source encoding. Results are presented which show LMS may provide almost 2 bits per symbol reduction in transmitted bit rate compared to DPCM when distortion levels are approximately the same for both methods. Alternatively, LMS can be used in fixed bit-rate environments to decrease the reconstructed image distortion. When compared with fixed coefficient DPCM, reconstructed image distortion is reduced by as much as 6-7 dB using LMS. Last, pictorial results representative of LMS processing are presented.}, number={3}, journal={IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING}, author={ALEXANDER, ST and RAJALA, SA}, year={1985}, pages={712–714} }
 @misc{alexander_1984, title={A DERIVATION OF THE COMPLEX FAST KALMAN ALGORITHM}, volume={32}, ISSN={["0096-3518"]}, DOI={10.1109/tassp.1984.1164470}, abstractNote={A derivation of a complex-domain recursive linear prediction algorithm with a reduced number of computations is presented. It is denoted the complex fast Kalman algorithm by virtue of its similarity to the real domain algorithm of that name. It is seen to be very similar to real domain fast Kalman, when complex conjugation is considered in formulating the error measure.}, number={6}, journal={IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING}, author={ALEXANDER, ST}, year={1984}, pages={1230–1232} }
 @article{alexander_a._1984, title={Optimal gain derivation for the LMS algorithm using a visual fidelity criteria}, volume={32}, DOI={10.1109/tassp.1984.1164322}, abstractNote={This paper analytically derives the optimal feedback gain parameter, ∞ 0 , for the least mean squares (LMS) algorithm used in a video compression application and subject to a visual fidelity criteria. Experimental results are presented which show these analytically derived values of ∞ 0 to be in excellent agreement with experimentally derived ∞ 0 over a wide range of filter and data parameters.}, journal={IEEE Transactions on Acoustics, Speech, and Signal Processing}, author={Alexander, S. T. and A., Rajala S.}, year={1984}, pages={434–437} }
 @misc{alexander_1983, title={Gravimeter}, volume={4,369,657}, number={1983 Jan. 25}, publisher={Washington, DC: U.S. Patent and Trademark Office}, author={Alexander, S. T.}, year={1983} }
 @article{satorius_alexander_1979, title={CHANNEL EQUALIZATION USING ADAPTIVE LATTICE ALGORITHMS}, volume={27}, ISSN={["0090-6778"]}, DOI={10.1109/tcom.1979.1094477}, abstractNote={In this paper, a study of adaptive lattice algorithms as applied to channel equalization is presented. The orthogonalization properties of the lattice algorithms make them appear promising for equalizing channels which exhibit heavy amplitude distortion. Furthermore, unlike the majority of other orthogonalization algorithms, the number of operations per update for the adaptive lattice equalizers is linear with respect to the number of equalizer taps.}, number={6}, journal={IEEE TRANSACTIONS ON COMMUNICATIONS}, author={SATORIUS, EH and ALEXANDER, ST}, year={1979}, pages={899–905} }