Optimum linear filtering of an integrated signal in white noise.
Optimum linear filtering of integrated signal in white noise, deriving expression for minimum mean square error
SIGNAL PROCESSING↗
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Results for “mean squared error”
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The adaptive prediction of time series.
Adaptive technique determination of optimum operations for pure prediction of discrete time series with respect to mean square error cost function
GAUSSIAN DISTRIBUTION↗
Determinable classes of channels.
Limitation imposed a priori on class of signals in order that every signal in class be distinguishable to within given mean square error by finite number of measurements
FUNCTION SPACE↗
Statistical inversion method for the solution of integral equations of the first kind
Statistical minimum root-mean-square error inversion method for solving integral equation of radiative heat transfer
Strand, O. N.↗
The state-variable approach to analog communication theory.
Approximate minimum mean square error estimates of Markovian state vector observed in nonlinearly imbedded stochastic signal, noting analog communication theory
Snyder, D. L.↗
A geometric treatment of the source encoding of a Gaussian random variable.
Source encoding of Gaussian random variable treated geometrically for minimum mean square error
Sakrison, D. J.↗
Information rates for data compression.
Upper and lower bounds on required information rate for data compression fidelity criterion, comparing bounds with equivalent mean-square-error result
Davisson, L. D.↗
Stochastic approximation algorithms for system identification, estimation, and decomposition of mixtures.
Stochastic approximation procedure minimizing mean square error criterion for system identification, estimation and decomposition of mixtures
Fu, K. S.↗
Optimum transmission of digital data by pulse code modulation.
Digital data transmission by pulse code modulation considered for minimum mean square error
Murthy, B. R. N.↗
An extended criterion for statistical linearization
Random-input describing function as linear approximation to instantaneous nonlinearity in terms of minimum mean-squared error
Curry, R. E.↗
Rate distortion function for a Gaussian source model of images
Gaussian source model of image, deriving rate distortion function under mean square error criterion
Habibi, A.↗
A rapidly converging first-order training algorithm for an adaptive equalizer
Rapidly converging first order training algorithm for adaptive equalizer design in PAM signal reception, using variable step sizes for mean- square error minimization
Schonfeld, T. J.↗
Delta Modulation
An optimum adaptive delta modulator-demodulator configuration is derived. This device utilizes two past samples to obtain a step size which minimizes the mean square error for a Markov Gaussian source. The optimum system is compared using computer simulations with the linear delta modulator and an enhanced Abate delta modulator. In addition the performance is compared to the rate distortion bound for a Markov source. It is shown that the optimum delta modulator is neither quantization nor slope-overload limited. The results show that the output signal-to-noise ratio is independent of the input signal power and is subject only to the limitations of the hardware employed. In addition, voice was recorded using these systems. The demodulated voice indicates negligible degradation is caused by the optimum system and by the enhanced Abate system while the linear delta modulator suffers significant degradation at a sampling frequency of 56 kilobits/sec.
Schilling, D. L.↗
Robust delta modulation.
A new Robust Delta Modulator configuration is presented. The system is optimum in the sense of minimizing the mean square error. Under certain conditions it is shown that the optimum system reduces to an enhanced Abate scheme. The optimum system, obtained by Song, uses the polarity of the past two samples and the signal estimates, to obtain the appropriate step size. Since the signal statistics are estimated by the system they are not needed a priori. The system has been constructed and tested. Experimental pictures and voice tapes are presented.
Song, C. L.↗
A variable-step-size robust delta modulator.
Description of an analytically obtained optimum adaptive delta modulator-demodulator configuration. The device utilizes two past samples to obtain a step size which minimizes the mean square error for a Markov-Gaussian source. The optimum system is compared, using computer simulations, with a linear delta modulator and an enhanced Abate delta modulator. In addition, the performance is compared to the rate distortion bound for a Markov source. It is shown that the optimum delta modulator is neither quantization nor slope-overload limited. The highly nonlinear equations obtained for the optimum transmitter and receiver are approximated by piecewise-linear equations in order to obtain system equations which can be transformed into hardware. The derivation of the experimental system is presented.
Song, C. L.↗
Linear restoration of incoherently radiating objects.
Light from an incoherently radiating object and background light are focused onto a photosensitive mosaic, the currents from whose elements constitute the data on which is based a least-squares linear estimate of the radiance at points in the object. By comparison of the mean-square error with that given by Wiener filtering theory, the equivalent noise spectral density for use in the latter is shown to consist of a shot-noise term and a term due to the random fluctuations of the incoherent light; the former predominates under most circumstances. Turbulent distortion of the image after passage of the rays through a random-phase screen is also treated from this standpoint.
Helstrom, C. W.↗
Dynamic programming training period for an MSE adaptive equalizer.
A steepest descent variable step-size algorithm has been designed using dynamic programming for a mean-square-error adaptive equalizer. Additive noise and a constraint have been included. It is found that the new algorithm converges faster than the common fixed step-size algorithm.
Richman, S. H.↗
Bayesian recursive image estimation.
The enhancement of images that are characterized only by statistical data where the picture contains additive noise is considered. The random process representing the output of the scanner is characterized by the output of a dynamic system with white noise input. The dynamic system describes a first-order vector-Markov process. The procedure of Kalman filtering is then utilized to recursively determine the minimum mean-square error estimate of the image. The result is then extended to obtain the smoothing of the data.
Nahi, N. E.↗