This paper presents an integer preserving (IP) version of the Levinson algorithm to solve a normal set of equations for a Hermitian Toeplitz matrix with any singularity profile. The IP property means that for a matrix with integer entries, the algorithm can be completed over the integer solely by using a ring of integer operations. The IP algorithm provides remedies for unpredictable numerical outcomes when a corresponding floating-point (FP) Levinson algorithm either overlooks zero principal minors (PMs) or applies a singularity skipping routine to a PM that is considered erroneously to be zero. The error-free computational edge of integer arithmetic is also applicable to a non-integer Toeplitz matrix by first scaling it up to an acceptably accurate integer matrix. The proposed algorithm can also be used to obtain the inverse of a nonsingular Hermitian Toeplitz matrix (with any singularity profile) by one of two proposed IP Gohberg-Semencul type inversion formulas.

The generalization of the Routh stability test to the corresponding zero location problem of determining how many of the zeros of a polynomial have negative real parts, positive real parts, or are purely imaginary encountered intensive and controversial activity about overcoming singular cases. This paper revisits this problem and presents two (MaxQ and LinQ) ZL methods for an arbitrary complex polynomial. The first method produces for an investigated polynomial$P(s)$of degree$n$a sequence of length$\leq n+1$of para-even or para-odd (para-paritic) polynomials of descending degrees obtained by a polynomial remainder routine with quotients ofmaximaldegrees. The second method uses successivelylinearquotients for the reduction of degrees and thus assign to$P(s)$always a sequence of exactly$n+1$para-paritic polynomials. Previous so-called first-type singularities become “non-essential singularities” in the sense that they are now absorbed into modified forms of the polynomial recursions. The distribution of zeros with respect to the imaginary axis is extracted in both methods by sign variation rules posed on the leading coefficients (that stay real when testing a complex polynomial as well) of the polynomials in the sequence.

This paper presents two efficient algorithms to determine whether a bivariate polynomial, possibly with complex coefficients, does not vanish in the cross product of two closed right-half planes (is “2-C stable”). A 2-C stable polynomial in the denominator of a two-dimensional analog filter has been proved (not long ago) to imply bounded-input bounded-output (BIBO) stability. The two algorithms are entirely different but both rely on a recently proposed fraction-free (FF) Routh test for complex polynomials in this transaction. The first algorithm tests the 2-C stability of a bivariate polynomial of degree (n1,n2) in order n6of elementary operations (when n1=n2=n). It is a “tabular type” two-dimensional stability test that can be regarded as a “Routh table” whose scalar entries were replaced by univariate polynomials. The second 2-C stability test is obtained from the first by its telepolation. It carries out the 2-C stability test by a finite collection of FF Routh tests and requires only order n4elementary operations. Both algorithms possess an integer-preserving property that enhances them with additional merits including numerical error-free decision on 2-C stability.

This paper presents an efficient and integer preserving procedure to decide whether a bivariate polynomial does not vanish in the cross product of two closed right half planes. The problem arises in testing the stability of two-dimensional continuous-time linear systems. The procedure is obtained by combining a recent fraction-free Routh stability test for complex univariate polynomials with the long known Ansell's conditions for stability of bivariate continuous-time system polynomials.

Gaussian mixture models (GMMs) are widely used in speech and speaker recognition. This study explores the idea that a mixture of skew Gaussians might capture better feature vectors that tend to have skew empirical distributions. It begins with deriving an expectation maximisation (EM) algorithm to train a mixture of two‐piece skew Gaussians that turns out to be not much more complicated than the usual EM algorithm used to train symmetric GMMs. Next, the algorithm is used to compare skew and symmetric GMMs in some simple speaker recognition experiments that use Mel frequency cepstral coefficients (MFCC) and line spectral frequencies (LSF) as the feature vectors. MFCC are one of the most popular feature vectors in speech and speaker recognition applications. LSF were chosen because they exhibit significantly more skewed distribution than MFCC and because they are widely used [together with the related immittance spectral frequencies (ISF)] in speech transmission standards. In the reported experiments, models with skew Gaussians performed better than models with symmetric Gaussians and skew GMMs with LSF compared favourably with both skew symmetric and symmetric GMMs that used MFCC.

Simplification of mixture models has recently emerged as an important issue in the field of statistical learning. The heavy computational demands of using large order models drove researches to investigate how to efficiently reduce the number of components in mixture models. The simplification, in solutions proposed so far, was performed by maximizing a certain measure of similarity to the original model, regardless of the discriminative qualities among models of different classes. This paper proposes a novel discriminative learning algorithm for reducing the order of a set of mixture models. The suggested algorithm is based on maximizing the correct component association. Experiments, performed on acoustic modeling in a basic phone recognition task, indicate that the proposed algorithm outperforms the comparable non-discriminative simplification algorithm.

The paper considers Levinson algorithms for Hermitian and non-Hermitian Toeplitz matrices that for integer matrices remain fraction-free (FF). A recently introduced FF algorithm is extended from Hermitian to non-symmetric Toeplitz matrices. An alternative proof for the integer-preservation property is obtained by linking the elements of the solution vectors to minors of the Toeplitz matrix. These links are also used to prove that the length of integers grows at a very restrained rate, a property that implies that the algorithms are very efficient integer algorithms.

This paper presents a new version for the classical Levinson algorithm for solution of a symmetric (Hermitian) Toeplitz set of equations. The new version has the property that for a Toeplitz matrix with (Gaussian) integer entries the algorithm is carried out entirely over integers. The new algorithm has a low binary complexity with a near-linear integer growth rate. The integer preserving property provides an immediate means to control the numerical accuracy of the solution and its associated triangular factorization. It is also more attractive for symbolic computation.

The paper considers a Gaussian-integer preserving (GIP) form for the author's method to test whether a polynomial with complex coefficients has its zeros inside the unit-circle (is 'stable'). The GIP property describes the fact that for a polynomial with Gaussian integer (i.e. "complex integer") coefficients, the test is carried out completely over Gaussian integers. The proposed algorithm has linear growth of the size of coefficients and an implied low binary complexity. This property is advantageous for deriving simpler stability constraints on designable parameters. It can also be exploited to reduce obstruction of decision about stability that can be introduced by numerical inaccuracy when testing ill-conditioned or high degree polynomials

The paper revises and simplifies Jury's tabular stability test for two-dimensional (2-D) discrete-time systems. The tabular test builds for a 2-D polynomial of degree (n/sub 1/, n/sub 2/) a '2-D table'-a sequence of n/sub 2/ matrices or equivalently 2-D polynomials and then examines its last entry-a 1-D polynomial of degree 2n/sub 1/n/sub 2/ for no zeros on the unit circle. Analysis of the cost of computation for the test is performed and shows that it is of O(n/sup 6/) (n/sub 1/=n/sub 2/=n), compared to previous tabular tests of exponential complexity. Next, we propose a new test based on telepolation-telescoping the last entry of this 2-D table by interpolation. The table's construction is replaced by n/sub 1/n/sub 2/+1 stability tests of 1-D polynomials of degree n/sub 1/ or n/sub 2/. The resulting new 2-D stability test is shown to require a low O(n/sup 4/) count of operations.

We are interested in automatically detecting specific phone segments that have been mispronounced by a nonnative student of a foreign language. The phone-level information allows a language instruction system to provide the student with feedback about specific pronunciation mistakes. Two approaches were evaluated; in the first approach, log-posterior probability-based scores [1] are computed for each phone segment. These probabilities are based on acoustic models of native speech. The second approach uses a phonetically labeled nonnative speech database to train two different acoustic models for each phone: one model is trained with the acceptable, or correct native-like pronunciations, while the other model is trained with the incorrect, strongly nonnative pronunciations. For each phone segment, a log-likelihood ratio score is computed using the incorrect and correct pronunciation models. Either type of score is compared with a phone dependent threshold to detect a mispronunciation. Performance of both approaches was evaluated in a phonetically transcribed database of 130,000 phones uttered in continuous speech sentences by 206 nonnative speakers.

A speech enhancement algorithm that is based on a connected-word hidden Markov model (HMM) is developed. Speech is assumed to be highly degraded by statistically independent additive noise. The minimum mean square error estimator is derived for a connected-word HMM. Further, we derive an estimator based on a connected-word HMM with explicit state duration. Listening experiments performed with digit strings have shown an increase of intelligibility. The best results were achieved when subjects who listened to the enhanced speech were given the results of an automatic recognition system.

A new algebraic test for two-dimensional digital filters is developed based on the author's stability test for one-dimensional discrete system polynomials with complex coefficients. The new method consists of an array of polynomials and an accompanying set of necessary and sufficient conditions for stability. Programming the construction of the array is simple and the execution involves a lower count of computation then reported for previous tests. Testing the stability conditions needs just a single "positivity test" of the last polynomial in the array plus standard 1-D stability conditions. A larger set of conditions necessary for stability that may be useful in other modes of application is also provided.

Several computationally efficient versions of the Levinson algorithm for solving linear equations with Toeplitz and quasi-Toeplitz matrices are presented, motivated by a new stability test. The new versions require half the number of multiplications and the same number of additions as the conventional form of the Levinson algorithm. The saving is achieved by using three-term (rather than two-term) recursions and propagating them in an impedance/admittance (or immittance) domain rather than the conventional scattering domain. One of the recursions coincides with recent results of P. Delsarte and Y. Genin (IEEE Trans., Acoust. Speech, Signal Proc., vol.ASSP-34, p.470-8, June 1986) on split Levinson algorithms for symmetric Toeplitz matrices, where the efficiency is gained by using the symmetric and skew-symmetric versions of the usual polynomials. This special structure is lost in the quasi-Toeplitz case, but one still can obtain similar computational reductions by suitably using three-term recursions in the immittance domain.>

Several lattice forms and algorithms which constitute the immittance domain alternatives to the PARCOR lattice algorithm are presented. The immittance variables were shown to offer more efficient Levinson algorithms than the conventional scattering algorithms for both symmetric and Hermitian Toeplitz matrices. This paper presents the lattices associated with the new recursions and provides algorithms to determine their coefficients directly from the signal segments. The new lattices are of interest for speech processing as they offer a different parametrization and process real signal segments with only one multiplier and two adders per section. Complex signal segments require two multipliers and adders per section. Stability conditions for the new parametrizations are also presented.

Several computationally extra-efficient versions of the Levinson algorithm are presented. The new versions require half the number of multiplications and the same number of additions as the conventional form of the Levinson algorithm. The saving is achieved by using three- (rather than two) term recursions and propagating them in an Impedance/Admittance domain rather than the conventional scattering domain. Our result apply both to Toeplitz and to close to Toeplitz systems. Moreover they provide a general method for reducing computational requirements in various recursive algorithm, e.g. adaptive least-square lattice algorithms.