The popular class of synchronizers that consist of a quadratic nonlinearity followed by a phase-lock loop is investigated, and it is shown that the optimum design of the quadratic transformation is characterized in te...
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The popular class of synchronizers that consist of a quadratic nonlinearity followed by a phase-lock loop is investigated, and it is shown that the optimum design of the quadratic transformation is characterized in terms of a spectral correlation function for the signal to be synchronized to. It is also shown that the SNR performance of this quadratic transformation, and the mean-square phase jitter of the phaselock loop are both characterized in terms of spectral correlation functions. The conditions under which the optimum quadratic transformations, for symbol synchronization of BPSK, QPSK, SQPSK, and MSK, and for carrier synchronization of BPSK, reduce to the well-known matched-filter-squarer are identified. In addition, the well-known zeromean-square-phase-jitter condition is generalized from PAM to all synchronizable signals, and is characterized in terms of the spectral correlation function. The low-SNR maximum-likelihood synchronizer for all quadratically synchronizable signals is characterized in terms of a multiplicity of maximum-SNR quadratic spectral-line generators. A closed form implementation in terms of a matched filter, squarer, and symbol-rate-synchronized averager is obtained for BPSK and QPSK signals.
Factor inverse matched filtering (FIMF) and factor inverse filtering (FIF) are signalprocessing techniques used to obtain desired signal responses. Both are especially useful procedures for ‘‘pulse‐compression’’...
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Factor inverse matched filtering (FIMF) and factor inverse filtering (FIF) are signalprocessing techniques used to obtain desired signal responses. Both are especially useful procedures for ‘‘pulse‐compression’’ processing and channel measurements. The theory is developed for a simple channel and known noise power spectral density so that comparison may be made with matched filtering. Expressions for the pulse‐compression energy gain, nonflatness loss NFL, and total performance are derived. The NFL is useful in selecting the best among practical pulse‐compression modulations, and with FIMF and FIF, has been used extensively since 1974 by the authors and their co‐workers in underwater acoustic propagation measurements and ocean acoustic tomography.
A layer stripping procedure for solving three‐dimensional Schrödinger equation inverse scattering problems is developed. This procedure operates by recursively reconstructing the Radon transform of the potential...
A layer stripping procedure for solving three‐dimensional Schrödinger equation inverse scattering problems is developed. This procedure operates by recursively reconstructing the Radon transform of the potential from the jump in the Radon transform of the scattered field at the wave front. This reconstructed potential is then used to propagate the wave front and scattered field differentially further into the support of the potential. The connections between this differential procedure and integral equation procedures are then illustrated by the derivations of two well known exact integral equation procedures using the Radon transform and a generalized Radon transform. These procedures, as well as the layer stripping procedure, are then reduced to the familiar Born approximation result for this problem by neglecting multiple scattering events. This illustrates the central role of the Radon transform in both exact and approximate inversion procedures.
This paper discusses the relationship between the zero crossings or zeros of band-limited signals and their nonlinear transformations. It is proved that the bandwidth of a signal can be compressed by a ratio of 1/ n i...
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This paper discusses the relationship between the zero crossings or zeros of band-limited signals and their nonlinear transformations. It is proved that the bandwidth of a signal can be compressed by a ratio of 1/ n if and only if the signal has n th-order zero crossings or zeros (if complex). Also, a monotonic nonlinearity in the observation of a band-limited signal can be identified from the zero crossings (or zeros) of the derivative of the observed signal. (The results are for one-dimensional signals. Extensions to two-dimensional signals remain to be addressed.)
A new algorithm for ray tracing parametric surface patches is presented. The method uses quasi-Newton iteration to solve for the ray/surface intersection and utilizes ray-to-ray coherence by using numerical informatio...
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This paper describes a technique for the enhancement of images by FIR filters which compensates for the decreased response of human vision at high spatial frequencies. Because many images contain mainly horizontal and...
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This paper describes a technique for the enhancement of images by FIR filters which compensates for the decreased response of human vision at high spatial frequencies. Because many images contain mainly horizontal and vertical features, and because vision is less acute along diagonals, it is possible to design anisotropic enhancement filters which do not increase greatly the background noise. The anisotropic design methodology also incorporates other results on filter design based on human vision which have recently been reported by the author and coworkers.
We propose a new, robust pitch detection algorithm for speech degraded by additive noise. Our algorithm exploits the high correlation between adjacent pitch periods that does not exist for the segment as a whole and p...
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We propose a new, robust pitch detection algorithm for speech degraded by additive noise. Our algorithm exploits the high correlation between adjacent pitch periods that does not exist for the segment as a whole and performs well in the vicinity of voiced/unvoiced regions where the local SNR is low. The algorithm works as follows. We first determine an estimate of the pitch period near the short time peak energy where the local SNR is highest. We then adaptively estimate the local pitch period from the peak towards the transition region by using pitch synchronous cross-correlation with an updated waveform. The performance of this new algorithm is compared to the SIFT and CEPSTRUM algorithms.
computer speech recognition is a discipline that has been viewed from two diametrically opposed perspectives. One perspective perceives recognition as a purely mathematical process; the other perceives it as an extens...
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computer speech recognition is a discipline that has been viewed from two diametrically opposed perspectives. One perspective perceives recognition as a purely mathematical process; the other perceives it as an extensive linguistical "knowledge" base. Because each perspective has its own set of limitations, neither approach has been able to achieve a viable machine realization of human auditory capabilities. Mathematical approaches do not perform fine phonetic distinctions well; linguistical approaches are not suitably machine oriented. We, therefore, propose in this paper a hybrid approach, suited both for machine implementation and for perceiving subtle differences in phonetic structure.
A comprehensive analysis of the mean-square learning characteristics of stochastic-descent algorithms is presented. The approach is based on the commonly exploited simplifying assumption of stationary independent trai...
A comprehensive analysis of the mean-square learning characteristics of stochastic-descent algorithms is presented. The approach is based on the commonly exploited simplifying assumption of stationary independent training vectors. Characteristics analyzed include stability, steady-state misadjustment, initial rate of convergence, optimum step size, and steady-state autocovariance and spectral characteristics of the weight-vector. Effects on these characteristics due to degree of randomness of stochastic gradient, particular data distribution, and data corruption are isolated and analyzed. An objective of the work is to keep the number of simplifying assumptions and approximations to a minimum. Comparison of results with previous more approximate analyses are made. Lernkurven von stochastischen Gradienten Algorithmen werden untersucht. Die vereinfachende Annahme von stationären, unabhängigen Trainingsvektoren wird benutzt. Charakteristiken die untersucht werden beinhalten Stabilität, ‘steady state’ Fehlanpassung, Start Konvergenz, optimaler Schritt sowie ‘steady state’ Autokovarianz und spektrale Charakteristik des Gewichtsvektors. Die Effekten auf diese Charakteristiken von dem Zufälligkeitsgrad des stichastischen Gradienten, besonderer Daten Verteilung und Daten Verderbung werden isoliert und analysiert. Ein Zielpunkt dieser Arbeit ist es die Anzahl vereinfachenden Annahmen und Approximationen auf ein minimum zu beschränken. Vergleiche mit Resultaten die von approximativeren Analysen stammen werden gezogen. Une analyse d'ensemble des caractéristiques de convergence de l'erreur quadratique moyenne dans les algorithmes utilisant la décroissance du gradient stochastique est presentée. Cette approche est basée sur l'hypothése simplificatrice classique de stationnarité et indépendance des vecteurs de test. Les caractéristiques analysées comprennent la stabilité, l'écart d'état stable, la vitesse initiale de convergence, le pas optimum d'incrémentation, et l'autocovarian
A study aimed at segmenting a high-resolution black and white image of Sunnyvale, California, is described. In this study regions were classified as belonging to any one of nine classes: residential, commercial/indust...
A study aimed at segmenting a high-resolution black and white image of Sunnyvale, California, is described. In this study regions were classified as belonging to any one of nine classes: residential, commercial/industrial, mobile home, water, dry land, runway/taxiway, aircraft parking, multilane highway, and vehicle parking. The classes were selected so that they directly relate to the Defense Mapping Agency's Mapping, Charting and Geodesy tangible features. To attack the problem a statistical segmentation procedure was devised. The primitive operators used to drive the segmentation are texture measures derived from cooccurrence matrices. The segmentation procedure considers three kinds of regions at each level of the segmentation: uniform, boundary, and unspecified. At every level the procedure differentiates uniform regions from boundary and unspecified regions. In the assigns a class label to the uniform regions. The boundary and unspecified regions are split to form higher level regions. The methodologies involved are mathematically developed as a series of hypothesis tests. While only a one-level segmentation was performed studies are described which show the capabilities of each of these hypothesis tests. In particular an 83% correct classification was obtained in testing the labeling procedure. These studies indicate that the proposed procedure should be useful for land use classifications as well as other problems.
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