Unsupervised learning for signal versus noise (Corresp.)

The Bayes solution to the unsupervised sequential learning problem induced by a mixture model for the two-class signal versus noise decision problem generates a computational and storage explosion. A quasi-Bayes approximate learning procedure is proposed that avoids the computational explosion while retaining the flavor of the Bayes solution. Convergence is established and efficiency is investigated.     

Detection of a coherent quantum signal in thermal noise (Corresp.)

Methods are presented for calculating the minimum attainable probability of error in detecting a coherent quantum signal received amid thermal noise in the limits of Iow and high signal-to-noise ratio. In the latter limit, quantum-mechanical perturbation theory is applied to solving the detection operator equation approximately. Graphical results are furnished for binary signals transmitted with equal prior probabilities. Previous work on this problem is thus extended to a broader range of signal and noise strengths. The results are applied to the detection of antipodal two-photon-coherent-state signals.     

On the output autocorrelation function of a single-valued nonlinearity with signal plus noise as input (Corresp.)

A method is given for obtaining series expansions for the coefficients in the double series for the autocorrelation function of the output of a nonlinearity with a signal plus noise as input. Two series are obtained, one in powers and the other in inverse powers of the signal-to-noise ratio. The terms in the series are products of two functions. In these series one function depends on the moments of the signal (or noise) and the other on characteristics of the nonlinearity and the noise (or signal). Differential recursion relationships that simplify evaluation of the nonlinearity-dependent functions are given.     

On the correlation function of signal plus Gaussian noise passed through nonlinear devices (Corresp.)

This correspondence discusses the transformations between the output autocorrelation functions of functionally related zero-memory nonlinear devices excited by signal plus Gaussian noise. The results are applied to show how output autocorrelation functions can easily be obtained for exponential and half-wave power law devices.     

Ungerboeck codes do not shape the signal power spectrum (Corresp.)

Simple sufficient conditions are found for the spectrum of Ungerboeck-coded signals to be equal to the spectrum of uncoded signals. It is shown that a carefully designed Ungerboeck code does not shape the spectrum.     

Zero-crossing rate for the sum of two sinusoids or a signal plus noise (Corresp.)

For the sum of two sinusoids of incommensurable frequencies, the number of zero-crossings per secondZis calculated. By averaging this result over a Rayleigh distribution for the amplitude of one of the sinusoids, Rice's formula is obtained for the numberzof zero-crossings per second of a sinusoid plus Ganssian noise of any spectrum. Simple approximations are obtained forzin the high-signal-to-noise-ratio and narrow-band cases. In addition, alternative derivations ofZandzare presented that further illuminate the significance of the foregoing results.     

An integral relevant to the detection of a signal in polarized Gaussian noise (Corresp.)

An integral is calculated that arises while determining the probability of detecting a signal in polarized Gaussian noise and the probability of hitting a particular elliptical target with an imperfect weapon.     

On the method of maximum entropy spectrum estimation (Corresp.)

We derive the method of maximum entropy spectrum estimation by bordering techniques of linear algebra. Using bordering, we obtain the recursive solution to the Yule-Walker equations and the recursive equation for the Toeplitz determinant in terms of the partial correlation coefficients. Minimization of the forward and backward predictor errors is then done with respect to the partial correlation coefficients. The minimization is done stagewise, constraining higher partial correlation values to zero. Thus, the minimization is done for a maximum-entropy normal process; the Toeplitz determinant is a maximum.     

Two-dimensional memoryless detection of a random signal inphi-mixing non-Gaussian noise (Corresp.)

The problem is considered of designing memoryless detection systems for detecting random signals in qb-mixing noise environments. Assuming that the bivariate densities of the noise can be expressed in an infinite series expansion, the nonlinearity is expressed as a series expansion and the coefficients are found that maximize the asymptotic relative efficiency.     

On estimating signal-to-noise ratio using the sample correlation coefficient (Corresp.)

Two versions of a Gaussian signal, corrupted by independent Gaussian noises, are available for estimating the signal-to-noise power ratio. This correspondence demonstrates that the sample correlation coefficient can be used to construct an unbiased estimator that is asymptotically efficient.     

Estimation of the Walsh spectrum (Corresp.)

In this work We investigate estimates of the Walsh spectrum of a dyadic-stationary series. We discuss the Walsh periodogram and smoothed periodogram computed from a stretch{X(t), t in [0, T]}of such a series.     

An adaptive digital filter for improving the signal-to-noise ratio of a signal with additive noise (Corresp.)

An adaptive digital filtering scheme is developed to deal with the problem of improving the signal-to-noise ratio of a signal corrupted by noise when only general {em a priori} assumptions regarding the signal and the noise are possible. Specifically, the noise is assumed to be white zero-mean and uncorrelated; while the signal is considered to be band-limited, possibly with slowly varying spectrum. The proposed adaptive digital filtering scheme is based upon a class of variable wave digital filters. Adaptation of the digital filter multipliers is accomplished through the use of an identification procedure based on an adaptive spectral estimation method.     

Deliberate noise in a modern cryptographic system (Corresp.)

Methods for incorporating deliberate noise into classical or public key cryptosystems are discussed.     

Poisson transform signal analysis (Corresp.)

It is shown that the Poisson transform used in the statistical theory of photodetection corresponds to a simple sign measurement and has mathematical properties which suggest its use in other areas of signal theory.     

Finite-memory algorithms for estimating the mean of a Gaussian distribution (Corresp.)

Let{X_n}_{n=1}^{infty}be independent random variables, each having amathcal{N}(mu, sigma^2)distribution. If we try to estimatemuwith anm-state learning algorithm, then the minimum mean-squared error is bounded below by that obtained by the bestm-level quantizer (which requires knowledge ofmu). Here we show that this lower bound is tight. The results are easily extended to a number of other problems, such as estimating the meanthetaof a uniform distribution.     

Power spectrum of FM clicks (Corresp.)

For the case of an unmodulated carrier, a simple approximate result is developed for the power spectral density of frequency-modulated (FM) clicks at the output of an ideal FM discriminator. In the baseband region the result agrees well with known exact results obtained by numerical integration at the threshold carrier-to-noise power ratio of10. Simple results are also presented for the bandwidth of FM clicks, the baseband noise power resulting from the FM clicks, and the total noise power associated with FM clicks.     

Formulas which approximate the distribution of a sinusoid plus noise (Corresp.)

The exact probability density function and cumulative distribution function of a sinusoid plus noise cannot in general be expressed in closed form. In this correspondence an approximation formula is derived that is applicable to any noise distribution since it is expressed solely in terms of the noise distribution itself. Its accuracy is checked against the Gaussian and Cauchy noise models.