A fast algorithm for LR-2 factorization of Toeplitz matrices

In this paper a new order recursive algorithm for the efficient −1 factorization of Toeplitz matrices is described. The proposed algorithm can be seen as a fast modified Gram-Schmidt method which recursively computes the orthonormal columns i, i = 1,2, …,p, of , as well as the elements of R−1, of a Toeplitz matrix with dimensions L × p. The factor estimation requires 8Lp MADS (multiplications and divisions). Matrix −1 is subsequently estimated using 3p2 MADS. A faster algorithm, based on a mixed and −1 updating scheme, is also derived. It requires 7Lp + 3.5p2 MADS. The algorithm can be efficiently applied to batch least squares FIR filtering and system identification. When determination of the optimal filter is the desired task it can be utilized to compute the least squares filter in an order recursive way. The algorithm operates directly on the experimental data, overcoming the need for covariance estimates. An orthogonalized version of the proposed −1 algorithm is derived. Matlab code implementing the algorithm is also supplied

The development of speech coding and the first standard coder for public mobile telephony

This thesis describes in its core chapter (Chapter 4) the original algorithmic and design features of the ??rst coder for public mobile telephony, the GSM full-rate speech coder, as standardized in 1988. It has never been described in so much detail as presented here. The coder is put in a historical perspective by two preceding chapters on the history of speech production models and the development of speech coding techniques until the mid 1980s, respectively. In the epilogue a brief review is given of later developments in speech coding. The introductory Chapter 1 starts with some preliminaries. It is de- ??ned what speech coding is and the reader is introduced to speech coding standards and the standardization institutes which set them. Then, the attributes of a speech coder playing a role in standardization are explained. Subsequently, several applications of speech coders - including mobile telephony - will be discussed and the state of the art in speech coding will be illustrated on the basis of some worldwide recognized standards. Chapter 2 starts with a summary of the features of speech signals and their source, the human speech organ. Then, historical models of speech production which form the basis of di??erent kinds of modern speech coders are discussed. Starting with a review of ancient mechanical models, we will arrive at the electrical source-??lter model of the 1930s. Subsequently, the acoustic-tube models as they arose in the 1950s and 1960s are discussed. Finally the 1970s are reviewed which brought the discrete-time ??lter model on the basis of linear prediction. In a unique way the logical sequencing of these models is exposed, and the links are discussed. Whereas the historical models are discussed in a narrative style, the acoustic tube models and the linear prediction tech nique as applied to speech, are subject to more mathematical analysis in order to create a sound basis for the treatise of Chapter 4. This trend continues in Chapter 3, whenever instrumental in completing that basis. In Chapter 3 the reader is taken by the hand on a guided tour through time during which successive speech coding methods pass in review. In an original way special attention is paid to the evolutionary aspect. Speci??cally, for each newly proposed method it is discussed what it added to the known techniques of the time. After presenting the relevant predecessors starting with Pulse Code Modulation (PCM) and the early vocoders of the 1930s, we will arrive at Residual-Excited Linear Predictive (RELP) coders, Analysis-by-Synthesis systems and Regular- Pulse Excitation in 1984. The latter forms the basis of the GSM full-rate coder. In Chapter 4, which constitutes the core of this thesis, explicit forms of Multi-Pulse Excited (MPE) and Regular-Pulse Excited (RPE) analysis-by-synthesis coding systems are developed. Starting from current pulse-amplitude computation methods in 1984, which included solving sets of equations (typically of order 10-16) two hundred times a second, several explicit-form designs are considered by which solving sets of equations in real time is avoided. Then, the design of a speci??c explicitform RPE coder and an associated eÆcient architecture are described. The explicit forms and the resulting architectural features have never been published in so much detail as presented here. Implementation of such a codec enabled real-time operation on a state-of-the-art singlechip digital signal processor of the time. This coder, at a bit rate of 13 kbit/s, has been selected as the Full-Rate GSM standard in 1988. Its performance is recapitulated. Chapter 5 is an epilogue brie y reviewing the major developments in speech coding technology after 1988. Many speech coding standards have been set, for mobile telephony as well as for other applications, since then. The chapter is concluded by an outlook

Immittance- versus scattering-domain fast algorithms for non-Hermitian Toeplitz and quasi-Toeplitz matrices

AbstractThe classical algorithms of Schur and Levinson are efficient procedures to solve sets of Hermitian Toeplitz linear equations or to invert the corresponding coefficient matrices. They propagate pairs of variables that may describe incident and scattered waves in an associated cascade-of-layered-media model, and thus they can be viewed as scattering-domain algorithms. It was recently found that a certain transformation of these variables followed by a change from two-term to three-term recursions results in reduction in computational complexity in the abovementioned algorithms roughly by a factor of two. The ratio of such pairs of transformed variables can be interpreted in the above layered-media model as an impedance or admittance; hence the name immittance-domain variables. This paper provides extensions for previous immittance Schur and Levinson algorithms from Hermitian to non-Hermitian matrices. It considers both Toeplitz and quasi-Toeplitz matrices (matrices with certain “hidden” Toeplitz structure) and compares two- and three-term recursion algorithms in the two domains. The comparison reveals that for non-Hermitian matrices the algorithms are equally efficient in both domains. This observation adds new comprehension to the source and value of algorithms in the immittance domain. The immittance algorithms, like the scattering algorithms, exploit the (quasi-)Toeplitz structure to produce fast algorithms. However, unlike the scattering algorithms, they can respond also to symmetry of the underlying matrix when such extra structure is present, and yield algorithms with improved efficiency

Sliding windows and lattice algorithms for computing QR factors in the least squares theory of linear prediction

Includes bibliographical references.In this correspondence we pose a sequence of linear prediction problems that differ a little from those previously posed. The solutions to these problems introduce a family of "sliding" window techniques into the least squares theory of linear prediction. By using these techniques we are able to QR factor the Toeplitz data matrices that arise in linear prediction. The matrix Q is an orthogonal version of the data matrix and the matrix R is a Cholesky factor of the experimental correlation matrix. Our QR and Cholesky algorithms generate generalized reflection coefficients that may be used in the usual ways for analysis, synthesis, or classification.This work was supported by the Office of Naval Research, Arlington, VA, under Contract N00014-85-K-0256

Ab initio calculation of the neutron-proton mass difference

The existence and stability of atoms rely on the fact that neutrons are more massive than protons. The measured mass difference is only 0.14\% of the average of the two masses. A slightly smaller or larger value would have led to a dramatically different universe. Here, we show that this difference results from the competition between electromagnetic and mass isospin breaking effects. We performed lattice quantum-chromodynamics and quantum-electrodynamics computations with four nondegenerate Wilson fermion flavors and computed the neutron-proton mass-splitting with an accuracy of $300$ kilo-electron volts, which is greater than $0$ by $5$ standard deviations. We also determine the splittings in the $\Sigma$, $\Xi$, $D$ and $\Xi_{cc}$ isospin multiplets, exceeding in some cases the precision of experimental measurements.Comment: 57 pages, 15 figures, 6 tables, revised versio

Optimisation techniques for low bit rate speech coding

This thesis extends the background theory of speech and major speech coding schemes used in existing networks to an implementation of GSM full-rate speech compression on a RISC DSP and a multirate application for speech coding. Speech coding is the field concerned with obtaining compact digital representations of speech signals for the purpose of efficient transmission. In this thesis, the background of speech compression, characteristics of speech signals and the DSP algorithms used have been examined. The current speech coding schemes and requirements have been studied. The Global System for Mobile communication (GSM) is a digital mobile radio system which is extensively used throughout Europe, and also in many other parts of the world. The algorithm is standardised by the European Telecommunications Standardisation histitute (ETSI). The full-rate and half-rate speech compression of GSM have been analysed. A real time implementation of the full-rate algorithm has been carried out on a RISC processor GEPARD by Austria Mikro Systeme International (AMS). The GEPARD code has been tested with all of the test sequences provided by ETSI and the results are bit-exact. The transcoding delay is lower than the ETSI requirement. A comparison of the half-rate and full-rate compression algorithms is discussed. Both algorithms offer near toll speech quality comparable or better than analogue cellular networks. The half-rate compression requires more computationally intensive operations and therefore a more powerful processor will be needed due to the complexity of the code. Hence the cost of the implementation of half-rate codec will be considerably higher than full-rate. A description of multirate signal processing and its application on speech (SBC) and speech/audio (MPEG) has been given. An investigation into the possibility of combining multirate filtering and GSM fill-rate speech algorithm. The results showed that multirate signal processing cannot be directly applied GSM full-rate speech compression since this method requires more processing power, causing longer coding delay but did not appreciably improve the bit rate. In order to achieve a lower bit rate, the GSM full-rate mathematical algorithm can be used instead of the standardised ETSI recommendation. Some changes including the number of quantisation bits has to be made before the application of multirate signal processing and a new standard will be required

Precision Light Flavor Physics from Lattice QCD

In this thesis we present three distinct contributions to the study of light flavor physics using the techniques of lattice QCD. These results are arranged into four self-contained papers. The first two papers concern global fits of the quark mass, lattice spacing, and finite volume dependence of the pseudoscalar meson masses and decay constants, computed in a series of lattice QCD simulations, to partially quenched SU(2) and SU(3) chiral perturbation theory (χPT). These fits determine a subset of the low energy constants of chiral perturbation theory — in some cases with increased precision, and in other cases for the first time — which, once determined, can be used to compute other observables and amplitudes in χPT. We also use our formalism to self-consistently probe the behavior of the (asymptotic) chiral expansion as a function of the quark masses by repeating the fits with different subsets of the data. The third paper concerns the first lattice QCD calculation of the semileptonic K0 → π −` +ν` (K`3) form factor at vanishing momentum transfer, f Kπ + (0), with physical mass domain wall quarks. The value of this form factor can be combined with a Standard Model analysis of the experimentally measured K0 → π −` +ν` decay rate to extract a precise value of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vus, and to test unitarity of the CKM matrix. We also discuss lattice calculations of the pion and kaon decay constants, which can be used to extract Vud through an analogous Standard Model analysis of experimental constraints on leptonic pion and kaon decays. The final paper explores the recently proposed exact one flavor algorithm (EOFA). This algorithm has been shown to drastically reduce the memory footprint required to simulate single quark flavors on the lattice relative to the widely used rational hybrid Monte Carlo (RHMC) algorithm, while also offering modest O(20%) speed-ups. We independently derive the exact one flavor action, explore its equivalence to the RHMC action, and demonstrate that additional preconditioning techniques can be used to significantly accelerate EOFA simulations. We apply EOFA to the ongoing RBC/UKQCD calculation of the ∆I = 1/2 K → ππ decay amplitude, and demonstrate that, in this context, gauge field configurations can be generated a factor of 4.2 times faster using an EOFAbased simulation rather than the previous RHMC-based simulations. We expect that EOFA will help to significantly reduce the statistical error in the first-principles determination of the Standard Model CP-violation parameters ε and ε′ offered by the K → ππ calculation