High-speed decoding technique for slip detection in data transmission systems using modified cyclic block codes

An efficient method is described for evaluating the error-checking syndrome for systems which are modified cyclic or shortened cyclic codes to detect slips of block synchronisation.     

Square root covariance ladder algorithms

Square root normalized ladder algorithms provide an efficient recursive solution to the problem of multichannel autoregressive model fitting. A simplified derivation of the general update formulas for such ladder forms is presented, and is used to develop the growing memory and sliding memory covariance ladder algorithms. New ladder form realizations for the identified models are presented, leading to convenient methods for computing the model parameters from estimated reflection coefficients. A complete solution to the problem of possible singularity in the ladder update equations is also presented.     

The second-order moments of the sample covariances for time serieswith missing observations

The estimation of the covariances of a stationary time series with missing observations is considered. General formulas for the asymptotic second-order moments of the sample covariances of such a time series are given for either random or deterministic patterns of misses. Closed-form expressions are derived for the random Bernoulli pattern and for the deterministic periodic pattern of missing observations and are explicitly evaluated for autoregressive moving-average time series. These results are useful for constructing and analyzing parameter or spectrum estimation algorithms based on the sample covariances for a stationary time series with missing observations     

Bounds on the accuracy of Gaussian ARMA parameter estimation methods based on sample covariances

The asymptotic accuracy of Gaussian ARMA parameter estimation methods based on a fixed number of sample covariances is considered. Several key results are briefly reviewed, including: i) a general asymptotic expression for the error covariance of the ARMA parameter estimates; ii) the fact that this error covariance is always greater than a certain lower bound; iii) the fact that this lower bound is strictly greater than the Cramer-Rao bound; iv) an explicit ARMA estimation technique that asymptotically achieves the bound. The key result of this note is a proof that this lower bound approaches the Cramer-Rao bound as the number of sample covariances tends to infinity.     

Computer image generation for flight simulators: the Gabor approach

A formalism for image representation in the combined frequency-position space is presented using the generalized Gabor approach. This approach uses elementary functions to which the human visual system is particularly sensitive and which are efficient for the analysis and synthesis of visual imagery. The formalism is also compatible with the implementation of a variable resolution system wherein image information is nonuniformly distributed across the visual field in accordance with the human visual system's ability to process it. When used with a gaze-slaved visual display system, imagery generated using the techniques described here affords a combination of high resolution and wide field-of-view. This combination is particularly important in high-fidelity, computergenerated, visual environments as required, for instance, in flight simulators.     

On the computation of an asymptotic bound for estimating autoregressive signals in white noise

The Cramer-Rao lower bound (CRLB) provides a useful reference for evaluating the performance of parameter estimation techniques. This paper considers the problem of estimating the parameters of an autoregressive signal corrupted by white noise. An explicit formula is derived for computing the asymptotic CRLB for the signal and noise parameters. Formulas for the asymptotic CRLB for functions of the signal and noise parameters are also presented. In particular, the center frequency, bandwidth and power of a second order process are considered. Some numerical examples are presented to illustrate the usefulness of these bounds in studying estimation accuracy.     

Performance analysis of parameter estimation algorithms based on high-order moments

Recently, there has been a considerable interest in parametric estimation of non-Gaussian processes, based on high-order moments. Several researchers have proposed algorithms for estimating the parameters of AR, MA and ARMA processes, based on the third-order and fourth-order cumulants. These algorithms are capable of handling non-minimum phase processes, and some of them provide a good trade-off between computational complexity and statistical efficiency. This paper presents some results about the performance of algorithms based on high-order moments. A general lower bound is derived for the variance of estimates based on high-order sample moments. This bound, which is shown to be asymptotically tight, is neither the Cramer-Rao bound nor a trivial extension thereof. The performance of weighted least squares estimates of the type recently proposed in the literature is investigated. An expression for the variance of such estimates is derived and the existence of an optimal weight matrix is proven. The general formulae are specialized to MA and ARMA processes and used to analyse the performance of some algorithms in detail. The analytic results are verified by Monte Carlo simulations for some specific test cases. A by-product of this paper is the derivation of asymptotic formulae for the variances and covariances of the sample third-order moments of a certain class of processes.     

Enhanced-resolution image restoration from a sequence of low-frequency vibrated images by use of convex projections

An algorithm to increase the spatial resolution of digital video sequences captured with a camera that is subject to mechanical vibration is developed. The blur caused by vibration of the camera is often the primary cause for image degradation. We address the degradation caused by low-frequency vibrations (vibrations for which the exposure time is less than the vibration period). The blur caused by low-frequency vibrations differs from other types by having a random shape and displacement. The different displacement of each frame makes the approach used in superresolution (SR) algorithms suitable for resolution enhancement. However, SR algorithms that were developed for general types of blur should be adapted to the specific characteristics of low-frequency vibration blur. We use the method of projection onto convex sets together with a motion estimation method specially adapted to low-frequency vibration blur characteristics. We also show that the random blur characterizing low-frequency vibration requires selection of the frames prior to processing. The restoration performance as well as the frame selection criteria is dependent mainly on the motion estimation precision.     

Molar Heat Capacity Cv, Vapor Pressure, and (p, ρ, T) Measurements from 92 to 350 K at Pressures to 35 MPa and a New Equation of State for Chlorotrifluoromethane (R13)

Measurements of the molar heat capacity at constant volume C _v for chlorotrifluoromethane (R13) were conducted using an adiabatic method. Temperatures ranged from 95 to 338 K, and pressures were as high as 35 MPa. Measurements of vapor pressure were made using a static technique from 250 to 302 K. Measurements of (p, , T) properties were conducted using an isochoric method; comprehensive measurements were conducted at 15 densities which varied from dilute vapor to highly compressed liquid, at temperatures from 92 to 350 K. The R13 samples were obtained from the same sample bottle whose mole fraction purity was measured at 0.9995. A test equation of state including ancillary equations was derived using the new vapor pressures and (p, , T) data in addition to similar published data. The equation of state is a modified Benedict–Webb–Rubin type with 32 adjustable coefficients. Acceptable agreement of C _v predictions with measurements was found. Published C _v(, T) data suitable for direct comparison with this study do not exist. The uncertainty of the C _v values is estimated to be less than 2.0% for vapor and 0.5% for liquid. The uncertainty of the vapor pressures is 1 kPa, and that of the density measurements is 0.1%.     

Reliable Collision Detection for Time-Dependent Parametric Surfaces

We improve on an algorithm by Von Herzen, Barr, and Zatz (HBZ) to detect geometric collisions between pairs of time-dependent parametric surfaces. The HBZ algorithm uses upper bounds on the parametric derivatives to guarantee detection of collisions and near misses, thus avoiding the defects of algorithms which sample the surfaces, possibly missing sharp spikes. Unfortunately, the user of the HBZ algorithm must supply not only routines computing the surface functions, but also routines bounding every component in the Jacobian of these surface functions over an arbitrary parametric range. Although they give helpful analyses for several types of surfaces, HBZ admit the need to provide Jacobian bounding routines as a disadvantage.We propose using interval arithmetic to bound functional values over a parametric input range, thus eliminating the need for the Jacobian entirely. Our interval version of the collision detection algorithm assumes neither bounded differentiability nor satisfaction of the Lipschitz criterion. Therefore, our code can detect geometric collisions for the much larger class of surface functions for which bounds on the function values can be computed using interval arithmetic. We contrast our code to that of HBZ and give timing comparisons.