design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

on high relative accuracy of the kogbetliantz method the relative accuracy of the kogbetliantz method for computing the singular value decomposition of real triangular matrices is considered sharp relative error bounds for the computed singular values are derived the results are obtained by estimating the norms of scaled perturbation matrices arising from errors generated in one step and one batch of commuting transformations perturbation matrices are scaled either from the left or right side by the inverse of the diagonal matrix

redundant cordic methods with a constant scale factor for sine and cosine computation proposes two redundant cordic coordinate rotation digital computer methods with a constant scale factor for sine and cosine computation called the double rotation method and the correcting rotation method in both methods the cordic is accelerated by the use of a redundant binary number representation as in the previously proposed redundant cordic in the proposed methods since the number of rotation extensions performed for each angle is a constant the scale factor is a constant independent of the operand hence one does not need to calculate the scale factor during the computation and can make a more efficient sine and cosine generator than that based on the previous redundant cordic

trends in systolic and cellular computation abstract a profile is given of current research as it pertains to computational mathematics on very large scale integration vlsi array processors in this type of parallel computers the cells of the array operate in single instruction multiple data simd mode and algorithms are executed in systolic or cellular fashion the focus of the presentation is on linear algebraic techniques a systolization process is illustrated by matching an arbitrary gaxpy operation onto a fixed size square array processor two recent systolic methods for solving systems of linear equations one iterative and the other direct are described a cellular algorithm for a fast fourier transform based on a new implementation on rectangular array processors of the perfect shuffle permutation is then derived using annotated lists of recent references snapshots of active research areas are given on systolic linear solvers the singular value decomposition artificial neural networks and the simulated annealing algorithm

frequency selective harmonic coding the present invention relates to a method of encoding speech comprised of processing the speech by harmonic coding to provide a fundamental frequency signal and a set of optimal harmonic amplitudes processing the harmonic amplitudes and the fundamental frequency signal to select a reduced number of bands and to provide for the reduced number of bands a voiced and unvoiced decision signal an optimal subset of magnitudes and a signal indicating the positions of the reduced number of bands whereby the speech signal may be encoded and transmitted as the pitch signal and the signals provided for the reduced number of bands with a bandwidth that is a fraction of the bandwidth of the speech

convergence to diagonal form of block jacobi type methods we provide sufficient conditions for the general sequential block jacobi type method to converge to the diagonal form for cyclic pivot strategies which are weakly equivalent to the column cyclic strategy given a block matrix partition a ij a i j of a square matrix mathbf a a the paper analyzes the iterative process of the form mathbf a k 1 mathbf p k mathbf a k mathbf q k a k 1 p k a k q k k ge 0 k 0 mathbf a 0 mathbf a a 0 a where mathbf p k p k and mathbf q k q k are elementary block matrices which differ from the identity matrix in four blocks two diagonal and the two corresponding off diagonal blocks in our analysis of convergence a promising new tool is used namely the theory of block jacobi operators typical applications lie in proving the global convergence of block jacobi type methods for solving standard and generalized eigenvalue and singular value problems

a systolic implementation of the chan foster rrqr algorithm the rank revealing qr factorization is a useful tool in many signal processing applications since it explicitly yields all the necessary information to solve rank deficient least squares problems and subset selection problems to compute signal and noise subspaces etc the authors present a systolic algorithm for computing a rank revealing qr factorization and consider the performance of the algorithm

an implicit jacobi like method for computing generalized hyperbolic svd abstract in this paper we introduce a joint hyperbolic orthogonal decomposition of two matrices which we call a generalized hyperbolic singular value decomposition or ghsvd this decomposition can be used for finding the eigenvalues and eigenvectors of a symmetric definite pencil x t x y t y where diag 1 we also present an implicit jacobi like method for computing this ghsvd

encoding and synthesis of tonal audio signals using dominant sinusoids and a vector quantized residual tonal signal tonal audio signals can be modeled as a sum of sinusoids with time varying frequencies amplitudes and phases an efficient encoder and synthesizer of tonal audio signals is disclosed the encoder determines time varying frequencies amplitudes and optionally phases for a restricted number of dominant sinusoid components of the tonal audio signal to form a dominant sinusoid parameter sequence these components are removed from the tonal audio signal to form a residual tonal signal the residual tonal signal is encoded using a residual tonal signal encoder rtse in one embodiment the rtse generates a vector quantization codebook vqc and residual codebook sequence rcs the vqc may contain time domain residual waveforms selected from the residual tonal signal synthetic time domain residual waveforms with magnitude spectra related to the residual tonal signal magnitude spectrum encoding vectors or a combination of time domain waveforms and magnitude spectrum encoding vectors the tonal audio signal synthesizer uses a sinusoidal oscillator bank to synthesize a set of dominant sinusoid components from the dominant sinusoid parameter sequence generated during encoding in one embodiment a residual tonal signal is synthesized using a vqc and rcs generated by the rtse during encoding if the vqc includes time domain waveforms an interpolating residual waveform oscillator may be used to synthesize the residual tonal signal the synthesized dominant sinusoids and synthesized residual tonal signal are summed to form the synthesized tonal audio signal

accuracy of two svd algorithms for 2 2 triangular matrices a new algorithm for the accurate computation of the singular value decomposition of 2x2 triangular matrices is proposed the algorithm is based on voevodin formulas sharp accuracy bounds are derived by using a subtle error analysis which tracks the signs of the errors of intermediate quantities and does not neglect the non linear parts of the errors the analysis is fine tuned for the case of almost diagonal matrices the same analysis is also used to analyze the errors for the xlasv2 computational routine of lapack the error estimates of the new algorithm compare favorably to those of the lapack routine

design of serially concatenated systems depending on the block length based on extrinsic information transfer exit charts the convergence behavior of iterative decoding is studied for a number of serially concatenated systems such as a serially concatenated code coded data transmission over an intersymbol interference channel bit interleaved coded modulation or trellis coded modulation efficient optimization algorithms based on simplified exit chart construction are devised to find irregular codes improving the convergence of iterative decoding one optimization criterion is to find concatenated systems exhibiting thresholds of successful decoding convergence which are close to information theoretic limits however these thresholds are approached only for very long block lengths to overcome this problem the decoding convergence after a fixed finite number of iterations is optimized which yields systems performing very well for short block lengths too as an example optimal system configurations for communication over an additive white gaussian noise channel are presented

computing the singular value decomposition on the connection machine consideration is given to the computation of the singular value decomposition svd on the connection machine cm brief descriptions of the lisp language and some typical matrix manipulating functions are given implementation details of various jacobi svd algorithms on an 8192 processor cm are presented for n n matrices where n

method for detection and correction of errors in speech pitch period estimates a method of detecting and correcting received values of a pitch period estimate of a speech signal for use in a speech coder or the like an average is calculated of the nonzero values of received pitch period estimate since the previous reset if a current pitch period estimate is within a range of 0 75 to 1 25 times the average it is assumed correct while if not a correction process is carried out if correction is required successively for more than a preset number of times which will most likely occur when the speaker changes the average is discarded and a new average calculated

convergence of scaled iterates by the jacobi method abstract a quadratic convergence bound for scaled iterates by the serial jacobi method for hermitian positive definite matrices is derived by scaled iterates we mean the matrices diag h k 1 2 h k diag h k 1 2 where h k k 0 are matrices generated by the method the bound is obtained in the general case of multiple eigenvalues it depends on the minimum relative separation of the eigenvalues

on quadratic convergence bounds for thej symmetric jacobi method this paper deals with quadratic convergence estimates for the serialj symmetric jacobi method recently proposed by veselic the method is characterized by the use of orthogonal and hyperbolic plane rotations using a new technique recently introduced by hari we prove sharp quadratic convergence bounds in the general case of multiple eigenvalues

extrinsic information transfer functions model and erasure channel properties extrinsic information transfer exit charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems a model is introduced that applies to decoding problems including the iterative decoding of parallel concatenated turbo codes serially concatenated codes low density parity check ldpc codes and repeat accumulate ra codes exit functions are defined using the model and several properties of such functions are proved for erasure channels one property expresses the area under an exit function in terms of a conditional entropy a useful consequence of this result is that the design of capacity approaching codes reduces to a curve fitting problem for all the aforementioned codes a second property relates the exit function of a code to its helleseth klove levenshtein information functions and thereby to the support weights of its subcodes the relation is via a refinement of information functions called split information functions and via a refinement of support weights called split support weights split information functions are used to prove a third property that relates the exit function of a linear code to the exit function of its dual

on the global convergence of the jacobi method for symmetric matrices of order 4 under parallel strategies abstract the paper analyzes special cyclic jacobi methods for symmetric matrices of order 4 only those cyclic pivot strategies that enable full parallelization of the method are considered these strategies unlike the serial pivot strategies can force the method to be very slow or very fast within one cycle depending on the underlying matrix hence for the global convergence proof one has to consider two or three adjacent cycles it is proved that for any symmetric matrix a of order 4 the inequality s a 2 1 10 5 s a holds where a 2 results from a by applying two cycles of a particular parallel method here s a stands for the frobenius norm of the strictly upper triangular part of a the result holds for two special parallel strategies and implies the global convergence of the method under all possible fully parallel strategies it is also proved that for every 0 and n 4 there exist a symmetric matrix a of order n and a cyclic strategy such that upon completion of the first cycle of the appropriate jacobi method the inequality s a 1 1 s a holds

a sort jacobi algorithm for semisimple lie algebras the classical jacobi algorithm is extended to an unified lie algebraic approach the conventional jacobi algorithm minimize the distance to diagonality they reduce the off norm i e the sum of squares of off diagonal entries sorting the diagonal elements after each step would accelerate the convergence but there are difficulties to apply this sorting to the off norm that has to minimize using the gradient flow of a trace function it r w brockett dynamical systems that sort lists diagonalize matrices and solve linear programming problems linear algebra appl 146 79 91 1991 zbl 0719 90045 as a more appropriate distance measure matrices can be diagonalized and the eigenvalues can be simultaneously sorted in this paper the sort jacobi algorithm is extended to a large class of structured matrices besides the semisimple lie algebra cases such as e g the symmetric hermitian and skew symmetric eigenvalue problem and the real and complex singular value decomposition par the local quadratic convergence of the sort jacobi method is proved for the regular case but not for the case in which the eigenvalues or singular values occur in clusters for these more complicated irregular problem a future publication is announced par the results are illustrated considering the lie algebra of derivations of the complex octonions

on the global and cubic convergence of a quasi cyclic jacobi method in this paper we consider the global and the cubic convergence of a quasi cyclic jacobi method for the symmetric eigenvalue problem the method belongs to a class of quasi cyclic methods recently proposed by w mascarenhas mascarenhas showed that the methods from his class asymptotically converge cubically per quasi sweep one quasi sweep is equivalent to 1 25 cyclic sweeps provided the eigenvalues are simple here we prove the global convergence of our method and derive very sharp asymptotic convergence bounds in the general case of multiple eigenvalues we discuss the ultimate cubic convergence of the method and present several numerical examples which all well comply with the theory

accuracy of the kogbetliantz method for scaled diagonally dominant triangular matrices the paper proves that kogbetliantz method computes all singular values of a scaled diagonally dominant triangular matrix which can be well scaled from both sides symmetrically to high relative accuracy special attention is paid to deriving sharp accuracy bounds for one step one batch and one sweep of the method by a simple numerical test it is shown that the methods based on bidiagonalization are generally not accurate on that class of well behaved matrices

a matrix pair of an almost diagonal skew symmetric matrix and a symmetric positive definite matrix abstract let a be skew symmetric b be symmetric positive definite and the pair a b have multiple eigenvalues if a is close to murnaghan form and b is close to diagonal form then certain principal submatrices of a and b are specially related in this paper we describe this relationship and quantify it under the usual asymptotic conditions if b i the identity matrix the result describes a special structure of a skew symmetric matrix almost in murnaghan form we then briefly discuss how the paardekooper method for skew symmetric matrices asymptotically behaves in the presence of multiple eigenvalues

voiced unvoiced information estimation system and method therefor a voiced unvoiced information estimation system uses input spectrum and synthetic spectrum to produce a voicing level spectrum the estimation system uses a spectrum difference calculation unit to normalize a spectrum difference energy for each harmonic band in unit of harmonic band and further uses a voicing level calculation unit to calculate a voicing level the voicing level of each harmonic band has a continuous value between 1 and 0 the estimation system is effective in vector quantization of voiced unvoiced information at a low bit rate because it is unnecessary to calculate a threshold for deciding a voiced unvoiced information a decision anomaly occurring due to threshold is eliminated and the accuracy of a voicing level is improved furthermore since a spectrum is represented by mixing a voiced element and a unvoiced element in a harmonic band the estimation system improves the audio quality of a combined sound

redundant and on line cordic for unitary transformations two sided unitary transformations of arbitrary 2 spl times 2 matrices are needed in parallel algorithms based on jacobi like methods for eigenvalue and singular value decompositions of complex matrices this paper presents a two sided unitary transformation structured to facilitate the integrated evaluation of parameters and application of the typically required transformations using only the primitives afforded by cordic thus enabling significant speedup in the computation of these transformations on special purpose processor array architectures implementing jacobi like algorithms we discuss implementation in nonredundant cordic to motivate and lead up to implementation in the redundant and on line enhancements to cordic both variable and constant scale factor redundant cfr cordic approaches are detailed and it is shown that the transformations may be computed in 10n spl delta time where n is the data precision in bits and spl delta is a constant accounting for accumulated on line delays a more area intensive approach using a novel on line cordic encoded angle summation difference scheme reduces computation time to 6n spl delta the area time complexities involved in the various approaches are detailed

system of analyzing human speech the pitch of human speech segments is analyzed using at least two different pitch detection algorithms a respective plurality of most likely values of pitch is selected by each of those algorithms and these values and their respective quality figures are analyzed statistically to determine the most likely pitch one algorithm operates in the frequency domain by analyzing an amplitude spectrum and the other algorithm operates in the time domain using an autocorrelation function significant peak positions of the amplitude spectrum or autocorrelation function are evaluated in respective harmonic sieves to provide respective quality figures indicating the degree to which peak frequency or period periods of the spectrum or autocorrelation function output match the apertures of the harmonic sieve a predetermined number of values of pitch and of period are selected having the highest quality figures after conversion of the values for period into values of pitch these values with their associated quality figures are analyzed statistically to form an estimation of the most likely pitch

redundant and on line cordic application to matrix triangularization and svd several modifications to the cordic method of computing angles and performing rotations are presented 1 the use of redundant carry free addition instead of a conventional carry propagate one 2 a representation of angles in a decomposed form to reduce area and communication bandwidth 3 the use of on line addition left to right digit serial addition to replace shifters by delays and 4 the use of online multiplication square root and division to compute scaling factors and perform the scaling operations the modifications improve the speed and the area of cordic implementations the proposed scheme uses efficiently floating point representations the application of the modified cordic method to matrix triangularization by givens rotations and to the computation of the singular value decomposition svd are discussed

the one bit null space learning algorithm and its convergence this paper proposes a new algorithm for mimo cognitive radio secondary users su to learn the null space of the interference channel to the primary user pu without burdening the pu with any knowledge or explicit cooperation with the su the knowledge of this null space enables the su to transmit in the same band simultaneously with the pu by utilizing separate spatial dimensions than the pu specifically the su transmits in the null space of the interference channel to the pu we present a new algorithm called the one bit null space learning algorithm obnsla in which the su learns the pu s null space by observing a binary function that indicates whether the interference it inflicts on the pu has increased or decreased in comparison to the su s previous transmitted signal this function is obtained by listening to the pu transmitted signal or control channel and extracting information from it about whether the pu s signal to interference plus noise power ratio sinr has increased or decreased the obnsla is shown to have a linear convergence rate and an asymptotic quadratic convergence rate finally we derive bounds on the interference that the su inflicts on the pu as a function of a parameter determined by the su this lets the su control the maximum level of interference which enables it to protect the pu completely blindly with minimum complexity the asymptotic analysis and the derived bounds also apply to the recently proposed blind null space learning algorithm

parallel singular value decomposition of complex matrices using multidimensional cordic algorithms the singular value decomposition svd of complex matrices is computed in a highly parallel fashion on a square array of processors using kogbetliantz s analog of jacobi s eigenvalue decomposition method to gain further speed new algorithms for the basic svd operations are proposed and their implementation as specialized processors is presented the algorithms are 3 d and 4 d extensions of the cordic algorithm for plane rotations when these extensions are used in concert with an additive decomposition of 2 spl times 2 complex matrices which enhances parallelism and with low resolution rotations early on in the svd process which reduce operation count a fivefold speedup can be achieved over the fastest alternative approach

method and system for determining the variation of a speech parameter for example the pitch in a speech signal in a method of and a system for determining the variation of a speech parameter for example the pitch in a speech signal values ms i j and coupling vectors v i j are calculated for time instants i and a number of values j of the speech parameter f j for each time instant i by means of an optimization algorithm of the values ms m j associated with the last time instant i m the optimum that is to say the smallest or on the contrary the largest value is determined by use of the coupling vectors the variation of the speech parameter as a function of time can be obtained by means of a back tracking procedure in the calculation of the values ms i j inter alia a cost parameter k is taken into account which is a measure of the deviation of the speech parameter f j i at the time instant i with respect to a predicted value for the speech parameter at the time instant i

asymptotic quadratic convergence of the serial block jacobi evd algorithm for hermitian matrices we provide the proof of the asymptotic quadratic convergence of the classical serial block jacobi evd algorithm for hermitian matrices with well separated eigenvalues including the multiple ones as well as clusters of eigenvalues at each iteration step two off diagonal blocks with the largest frobenius norm are eliminated which is an extension of the original jacobi approach to the block case numerical experiments illustrate and confirm the developed theory

short time fourier analysis of sampled speech the theoretical basis for the representation of a speech signal by its short time fourier transform is developed a time frequency representation for linear time varying systems is applied to the speech production model to formulate a quasi stationary representation for the speech waveform short time fourier analysis of the resulting representation yields the relationship between the short time fourier transform of the speech and the speech production model

coded sampling bound how much training is needed for iterative semi blind channel estimation coherent detection is commonly facilitated by means of pilot aided channel estimation while this approach offers a high estimation accuracy the spectral and power efficiencies are reduced due to the pilot overhead in the case that redundancy due to channel coding is not used for the purpose of channel estimation the maximum pilot spacing for which a time varying channel can be reconstructed without distortion is given by the nyquist shannon sampling theorem in this paper it is shown that if channel coding is taken into account for channel estimation in an iterative fashion the maximum spacing can be significantly extended which results in an increased spectral efficiency towards this goal a so called coded sampling bound is derived this semi analytical bound is compared with the nyquist shannon sampling theorem the presented results indicate that the maximum pilot spacing can be arbitrarily large given a suitable channel code and code rate

on pairs of almost diagonal matrices abstract the known results on almost diagonal hermitian matrices are generalized to deal with pairs of almost diagonal hermitian matrices the pairs are assumed to be definite or positive definite the obtained estimates are used to justify the failure of the quadratic convergence of jacobi methods for the generalized eigenvalue problem ax bx

quadratic convergence estimate of scaled iterates by j symmetric jacobi method abstract this paper estimates the quadratic convergence reduction of scaled iterates by j symmetric jacobi method numer math 64 1993 241 although the method is well defined for a general definite pair h j h ht j diag im in m the paper considers the most important case when h is positive definite in that case the method is an accurate floating point eigensolver for the pair h j as such it is used in a compound algorithm for accurate floating point computation of eigenvalues and eigenvectors of a non singular indefinite symmetric matrix the new result is proved for scaled diagonally dominant matrices in the general case of multiple eigenvalues it uses frobenius norm of the off diagonal part of symmetrically scaled iteration matrix and a relative gap in the spectrum of h j it can be effectively used in connection with stopping criterion of the method especially with its one sided version

singular value decomposition and improved frequency estimation using linear prediction linear prediction based lp methods for fitting multiple sinusoid signal models to observed data such as the forward backward fblp method of nuttall 5 and ulrych and clayton 6 are very ill conditioned the locations of estimated spectral peaks can be greatly affected by a small amount of noise because of the appearance of outliers lp estimation of frequencies can be greatly improved at low snr by singular value decomposition svd of the lp data matrix the improved performance at low snr is also better than that obtained by using the eigenvector corresponding to the minimum eigenvalue of the correlation matrix as is done in pisarenko s method and its variants

constant factor redundant cordic for angle calculation and rotation a constant factor redundant cordic cfr cordic scheme where the scale factor is kept constant while an angle for plane rotations is computed is developed the direction of rotation is determined from an estimate of the sign and convergence is assured by suitably placed correcting iterations the number of iterations in the cordic rotation unit is reduced by about 25 by expressing the direction of the rotation in radix 2 and radix 4 and conversion to conventional representation is done on the fly the performance of cfr cordic is estimated and compared with that of previously proposed schemes it is found to provide an execution time similar to that of redundant cordic with a variable scaling factor with a significant saving in area

on the quadratic convergence of kogbetliantz s algorithm for computing the singular value decomposition abstract it is shown that the cyclic kogbetliantz algorithm ultimately converges quadratically when no pathologically close singular values are present

iterative decoding of binary block and convolutional codes iterative decoding of two dimensional systematic convolutional codes has been termed turbo de coding using log likelihood algebra we show that any decoder can be used which accepts soft inputs including a priori values and delivers soft outputs that can be split into three terms the soft channel and a priori inputs and the extrinsic value the extrinsic value is used as an a priori value for the next iteration decoding algorithms in the log likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code the iteration is controlled by a stop criterion derived from cross entropy which results in a minimal number of iterations optimal and suboptimal decoders with reduced complexity are presented simulation results show that very simple component codes are sufficient block codes are appropriate for high rates and convolutional codes for lower rates less than 2 3 any combination of block and convolutional component codes is possible several interleaving techniques are described at a bit error rate ber of 10 sup 4 the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block convolutional component codes interleaver sizes less than 1000 and for three to six iterations

spectral magnitude representation for multi band excitation speech coders a method for encoding a speech signal into digital bits including the steps of dividing the speech signal into speech frames representing time intervals of the speech signal determining voicing information for frequency bands of the speech frames and determining spectral magnitudes representative of the magnitudes of the spectrum at determined frequencies across the frequency bands the method further includes quantizing and encoding the spectral magnitudes and the voicing information the steps of determining quantizing and encoding the spectral magnitudes is done is such a manner that the spectral magnitudes independent of voicing information are available for later synthesizing

quadratic convergence of scaled matrices in jacobi method a quadratic convergence bound for scaled jacobi iterates is proved provided the initial symmetric positive definite matrix has simple eigenvalues the bound is expressed in terms of the off norm of the scaled initial matrix and the minimum relative gap in the spectrum the obtained result can be used to predict the stopping moment in the two sided and especially in the one sided jacobi method

parallel and adaptive high resolution direction finding recently the new class of so called subspace methods for high resolution direction finding has received a great deal of attention in the literature when a real time implementation is aimed at the computational complexity involved is known to represent a serious impediment in this paper an esprit type algorithm is developed which is fully adaptive and therefore particularly suited for real time processing furthermore a systolic array is described which allows the processing of incoming data at a rate which is independent of the problem size the algorithm is based on orthogonal transformations only estimates are computed for the angles of arrival as well as for the source signals our aim is not so much to develop yet another esprit type algorithm but rather to show that it is indeed possible to develop an algorithm that is fully parallel and adaptive this is something that has not been done before

a systolic array for recursive least squares computations a triangular processor array has been developed for implementing recursive least squares computations the throughput is o n sup 0 which means that data vectors are fed in at a rate that is independent of the problem size the corresponding least squares solutions then run out of the array at the same rate the overall efficiency is roughly 67 this array is believed to be the first to implement a complete rls algorithm in a stable and efficient manner

annihilation reordering look ahead pipelined cordic based rls adaptive filters and their application to adaptive beamforming the novel annihilation reordering look ahead technique is proposed as an attractive technique for pipelining of givens rotation or cordic based adaptive filters unlike the existing relaxed look ahead the annihilation reordering look ahead does not depend on the statistical properties of the input samples it is an exact look ahead based on cordic arithmetic which is known to be numerically stable the conventional look ahead is based on multiply add arithmetic the annihilation reordering look ahead technique transforms an orthogonal sequential adaptive filtering algorithm into an equivalent orthogonal concurrent one by creating additional concurrency in the algorithm parallelism in the transformed algorithm is explored and different implementation styles including pipelining block processing and incremental block processing are presented their complexities are also studied and compared the annihilation reordering look ahead is employed to develop fine grain pipelined qr decomposition based rls adaptive filters both qrd rls and inverse qrd rls algorithms are considered the proposed pipelined architectures can be operated at arbitrarily high sample rate without degrading the filter convergence behavior stability under finite precision arithmetic are studied and proved for the proposed architectures the pipelined cordic based rls adaptive filters are then employed to develop high speed linear constraint minimum variance lcmv adaptive beamforming algorithms both qr decomposition based minimum variance distortionless response mvdr realization and generalized sidelobe canceller gsc realization are presented the complexity of the pipelined architectures are analyzed and compared the proposed architectures can be operated at arbitrarily high sample rate and consist of only givens rotations which can be scheduled onto cordic arithmetic based processors

a systolic array for recursive least squares computations mapping directionally weighted rls on an svd updating array a systolic algorithm array is described for recursive least squares rls estimation which achieves an o n sup 0 throughput rate with o n sup 2 parallelism the array is also useful for several other applications such as e g svd updating and kalman filtering an additional advantage is that unlike with other rls arrays it is now possible to incorporate alternative data weighting strategies such as directional weighting without sacrificing speed

a unified algebraic transformation approach for parallel recursive and adaptive filtering and svd algorithms in this paper a unified algebraic transformation approach is presented for designing parallel recursive and adaptive digital filters and singular value decomposition svd algorithms the approach is based on the explorations of some algebraic properties of the target algorithms representations several typical modern digital signal processing examples are presented to illustrate the applications of the technique they include the cascaded orthogonal recursive digital filter the givens rotation based adaptive inverse qr algorithm for channel equalization and the qr decomposition based svd algorithms all three examples exhibit similar throughput constraints there exist long feedback loops in the algorithms signal flow graph representation and the critical path is proportional to the size of the problem applying the proposed algebraic transformation techniques parallel architectures are obtained for all three examples for cascade orthogonal recursive filter retiming transformation and orthogonal matrix decompositions or pseudo commutativity are applied to obtain parallel filter architectures with critical path of five givens rotations for adaptive inverse qr algorithm the commutativity and associativity of the matrix multiplications are applied to obtain parallel architectures with critical path of either four givens rotations or three givens rotations plus two multiply add operations whichever turns out to be larger for svd algorithms retiming and associativity of the matrix multiplications are applied to derive parallel architectures with critical path of eight givens rotations the critical paths of all parallel architectures are independent of the problem size as compared with being proportional to the problem size in the original sequential algorithms parallelism is achieved at the expense of slight increase or the same for the svd case in the algorithms computational complexity

on the qr algorithm and updating the svd and the urv decomposition in parallel abstract a jacobi type updating algorithm for the svd or the urv decomposition is developed which is related to the qr algorithm for the symmetric eigenvalue problem the algorithm employs one sided transformations and therefore provides a cheap alternative to earlier developed updating algorithms based on two sided transformations the present algorithm as well as the corresponding systolic implementation is therefore rpughly twice as fast as the former method while the tracking properties are preserved the algorithm is also extended to the two matrix q svd or qurv case finally the differences with a number of closely related algorithms that have recently been proposed are discussed

electrolaryngeal speech enhancement for telephony a technique for separating an acoustic signal into a voiced v component corresponding to an electrolaryngeal source and an unvoiced u component corresponding to a turbulence source the technique can be used to improve the quality of electrolaryngeal speech and may be adapted for use in a special purpose telephone a method according to the invention extracts a segment of consecutive values from the original stream of numerical values and performs a discrete fourier transform on the this first group of values next a second group of values is extracted from components of the discrete fourier transform result which correspond to an electrolaryngeal fixed repetition rate f0 and harmonics thereof an inverse fourier transform is applied to the second group of values to produce a representation of a segment of the v component multiple v component segments are then concatenated to form a v component sample stream finally the u component is determined by subtracting the v component sample stream from the original stream of numerical values

on efficient implementations of kogbetliantz s algorithm for computing the singular value decomposition in this paper we compare several implementations of kogbetliantz s algorithm for computing the svd on sequential as well as on parallel machines comparisons are based on timings and on operation counts the numerical accuracy of the different methods is also analyzed

on the schur decomposition of a matrix for parallel computation an algorithm to solve the eigenproblem for nonsymmetric matrices on an n n array of mesh connected processors isomorphic to the architecture described by brent and luk for symmetric matrices is presented this algorithm is a generalization of the classical jacobi method and as such holds promise for parallel architectures the rotational parameters for the nonsymmetric case are carefully analyzed many examples of a working program simulating the parallel architecture are given with experimental evidence of quadratic convergence

method for determining the variation with time of a speech parameter and arrangement for carryin out the method in a speech or speaker recognition system a segment or sequence of speech parameter values are smoothed to a most probable sequency by dynamic programming the method for determining the variation with time of a speech parameter is based on a speech signal which is subdivided into successive segments and an individual value exists in each segment and for each value of the parameter within a limited range of values for the example of the fundamental voice frequency a value has been generated in each speech segment with the aid of the amdf average magnitude difference function the required variation now links a sequency of horizontally vertically or diagonally directly adjacent speech parameter values to one another in such a manner that the sum of the associated individual values represents a minimum in this arrangement this sum is slightly magnified in diagonal or vertical sections since a horizontal variation is most probable this magnification is controlled by certain fixed values which influence the smoothness of the variation

methods for generating the voiced portion of speech signals the pitch estimation method is improved sub integer resolution pitch values are estimated in making the initial pitch estimate the sub integer pitch values are preferably estimated by interpolating intermediate variables between integer values pitch regions are used to reduce the amount of computation required in making the initial pitch estimate pitch dependent resolution is used in making the initial pitch estimate with higher resolution being used for smaller values of pitch the accuracy of the voiced unvoiced decision is improved by making the decision dependent on the energy of the current segment relative to the energy of recent prior segments if the relative energy is low the current segment favors an unvoiced decision if high it favors a voiced decision voiced harmonics are generated using a hybrid approach some voiced harmonics are generated in the time domain whereas the remaining harmonics are generated in the frequency domain this preserves much of the computational savings of the frequency domain approach while at the same time improving speech quality voiced harmonics generated in the frequency domain are generated with higher frequency accuracy the harmonics are frequency scaled transformed into the time domain with a discrete fourier transform interpolated and then time scaled

on kogbetliantz s svd algorithm in the presence of clusters we consider matrices with off diagonal blocks of small norm and derive tight bounds for the approximation of their singular values by those of their diagonal blocks these results are used to show that triangular matrices with clusters of singular values must possess a principal submatrix of nearly diagonal form from the latter we then derive results pertaining to the quadratic convergence of kogbetliantz s algorithm for computing the svd in the presence of clusters

optimal placement of training for frequency selective block fading channels the problem of placing training symbols optimally for orthogonal frequency division multiplexing ofdm and single carrier systems is considered the channel is assumed to be quasi static with a finite impulse response of length l 1 samples under the assumptions that neither the transmitter nor the receiver knows the channel and that the receiver forms a minimum mean square error mmse channel estimate based on training symbols only training is optimized by maximizing a tight lower bound on the ergodic training based independent and identically distributed i i d capacity for ofdm systems it is shown that the lower bound is maximized by placing the known symbols periodically in frequency for single carrier systems under the assumption that the training symbols are placed in clusters of length spl alpha spl ges 2l 1 it is shown that the lower bound is maximized by a family of placement schemes called qpp spl alpha where qpp stands for quasi periodic placement these placement schemes are formed by grouping the known symbols into as many clusters as possible and then placing these clusters periodically in the packet for both ofdm and single carrier systems the optimum energy tradeoff between training and data is also obtained

on sharp quadratic convergence bounds for the serial jacobi methods using a new technique we derive sharp quadratic convergence bounds for the serial symmetric and svd jacobi methods for the symmetric jacobi method we consider the cases of well and poorely separated eigenvalues our result implies the result proposed but not correctly proved by van kempen it also extends the well known result of wilkinson to the case of multiple eigenvalues

triangular processor array for computing singular values a triangular processor array for computing the singular values of an m n m n matrix is proposed a jacobi type algorithm is used to first triangularize the given matrix and then diagonalize the resultant triangular form the requirements are 14n2 o n processors and o m ns time where s denotes the number of sweeps the triangular array can be extended to a rectangular one with 12mn o m processors for the computational of singular vectors

order recursive factorization of the pseudoinverse of a covariance matrix a numerically reliable algorithm is developed to recursively update the square root of a pseudoinverse matrix using the square root of a lower dimension pseudoinverse matrix the numerical computations are based on a generalized singular value decomposition which is used to do a canonical correlation analysis an operation count is given for sequential and parallel implementation of a partitioned order recursive algorithm these methods are useful for covariance analysis to determine the contributions due to various modeling errors in the design of a kalman filter

a proof of convergence for two parallel jacobi svd algorithms the authors consider two parallel jacobi algorithms due to r p brent et al j vlsi comput syst vol 1 p 242 70 1985 and f t luk 1986 j lin alg applic vol 77 p 259 73 for computing the singular value decomposition of an n n matrix by relating the algorithms to the cyclic by rows jacobi method they prove convergence of the former for odd n and of the latter for any n the authors also give a nonconvergence example for the former method for all even n or 4

linear convergence of the row cyclic jacobi and kogbetliantz methods linear convergence of the row cyclic jacobi and kogbetliantz methods can be guaranteed if certain constraints concerning the angles of rotations are implemented unlike the results of forsythe and henrici convergence can be achieved without under rotations