In previous studies of heart rate variability in humans, it has been demonstrated that the scale-dependent wavelet transform (WT) standard deviation [/spl sigma//sub wav/(m)] of the interbeat intervals can be used to discriminate patients with certain forms of cardiac dysfunction from normal subjects. This paper forges an explicit link between this measure and a corresponding spectral measure, which is also shown to provide discrimination between the two classes of data. The statistics of the estimator for /spl sigma//sub wav/(m) are obtained in the analytically simplest case, including expressions for its bias and variance. Numerical simulations are provided to support the theoretical analysis. We compare the bias, variance, and frequency resolution of the WT and spectral measures, and conclude that the former appears more suited to our particular circumstances.

A phase-noise-cancelled coherent subcarrier fiberoptic communication system that uses integrated-optic Mach-Zehnder waveguide modulators for frequency-pair encoding is introduced. Optical double-sideband suppressed-carrier signals with the same random phase noise and information encoded in the frequency separation of the two sidebands are generated by properly biasing the modulator. Phase noise is eliminated at the receiver by a nonlinear operation on the two sidebands. System performance analysis with numerical examples, taking into account the modulation index and laser normalized linewidth, is presented.

Two relatively simple renewal processes whose power spectral densities vary as 1/f/sup D/ are constructed: 1) a standard renewal point process, with 0>

Several methods have been proposed for the generation of photon-number-squeezed (sub-Poisson) light by imparting to the photon stream and anticorrelation that regularizes the times of arrival of the photons. This is accomplished by means of control of the excitation or emission process or by feedback, using a copy of the photon point processes when the emissions occur in parts. Possible advantages of communication by photon-number-squeezed light are discussed. For receivers in which the photon arrival times are observed, the channel capacity cannot be improved by modifying an initially Poisson photon stream and making it sub-Poisson. For photon-counting receivers, however, improvement of the channel capacity is possible. The bit-error-rate of an on-off keying communication system using sub-Poisson photons created by introducing anticorrelation into an initially Poisson beam may or may not be smaller than the error rates of the Poisson channel, depending on where the maximum power constraint is placed.>

In vertebrates, the excitation of the retinal rod photoreceptors by a single photon can be represented by a cyclic-GMP cascade. We construct a mathematical model for describing this mechanism and conduct a noise analysis of the process. Our results show that the relative noise of the rod photocurrent, which ensues from a filtering of the discrete multiplication process, is determined primarily by the first stage of the excitatory cascade. This stage is associated with the activation of transducin in the rod outer segment. Our analysis also shows that the conversion of the discrete multiplied signal into a current reduces the output relative noise when it is measured in terms of the variance-to-mean ratio.

The behavior of power-law shot noise, for which the associated impulse response functions assume a decaying power-law form, is explored. Expressions are obtained for the moments, moment generating functions, amplitude probability density functions, autocorrelation functions, and power spectral densities for a variety of parameters of the process. For certain parameters the power spectral density exhibits 1/f-type behavior over a substantial range of frequencies, so that the process serves as a source of 1/f/sup alpha / shot noise for alpha in the range 0>

For pt.IV see ibid., vol.SMC-13, no.5, p.964-72 (1983). The psychophysical properties of a multiple-channel neural-counting model are investigated. Each channel represents a peripheral afferent fiber (or a group of such fibers) and consists of a cascade of signal-processing transformations, each of which has a physiological correlate in the auditory system. The acoustic signal is passed by a mathematical construct (which may be a pure tone or Gaussian noise) through a series of transformations. Spontaneous neural activity is independently incorporated into each channel by means of an additive refractoriness-modified Poisson process. A union process at a more distal center in the nervous system is generated by a parallel collection of such channels with a density (in frequency) determined by the cochlear mapping function. The statistics of the union count (in a fixed time) are then processed at a decision center in a manner that depends on the psychophysical paradigm under consideration. This random count number is assumed to contain all of the information for the examples considered. The model has been used to calculate psychophysical functions for pure-tone loudness estimation, pure-tone and variable-bandwidth noise intensity discrimination, and variable-bandwidth noise loudness summation. The theoretical results are in good agreement with human psychophysical data.

A recurrence relation is obtained for the counting distribution, as well as the probability density of waiting time, for a doubly stochastic Poisson point process driven by nonstationary shot noise (SNDP). For a stimulus of short duration, the counting distribution approximately reduces to the Neyman Type-A. The SNDP is an important special Neyman-Scott cluster process.

An energy-based neural-counting model, incorporating refractoriness and spread of excitation, has recently been applied to intensity discrimination and loudness estimation for a variety of acoustic stimuli. In this model, refractoriness was the sole means of achieving the saturation effect of the afferent fiber's response. Though refractoriness (or an effect like it) should be included in a proper Poisson-based model to produce a neural count variance less than the count mean (in accordance with experiment), there is a strong additional saturation effect associated with the response of the receptor. This earlier model is now extended to incorporate the effects of receptor saturation and spontaneous neural activity. In this paper the behavior of individual neural channels is investigated. Theoretical firing-rate curves are obtained as a function of stimulus level and frequency (isointensity contours). These are found to be in good agreement with neurophysiological data. It is shown that it is possible to fit human psychophysical tuning curves with a double-tuned linear filter, by judicious choice of the tuning parameter Q.

The effect of nonparalyzable dead time on Poisson point processes with random integrated rates is studied. The case of exponentially decreasing rate, plus background (pedestal), with a uniformly uncertain starting time is explicitly presented. The decay time is considered to be slow compared to the refractory time. No constraints on the sampling time are imposed for calculating the mean and variance, though for the counting distribution, the sampling time must be short compared to the decay time. The results are expected to be useful in neurobiology, neural counting, psychophysics, photon counting, nuclear counting, and radiochemistry.

A single-threshold detector is derived for a wide class of classical binary decision problems involving the likelihood-ratio detection of a signal embedded in noise. The class of problems considered encompasses the case of multiple independent (but not necessarily identically distributed) observations of a nonnegative (or nonpositive) signal embedded in additive and independent noise, where the range of the signal and noise is continuous. It is shown that a comparison of the sum of the observations with a unique threshold comprises an optimum detector if a weak condition on the noise is satisfied independent of the signal. Examples of noise densities that satisfy and that violate this condition are presented. A sufficient condition on the likelihood ratio which implies that the sum of the observations is also a sufficient statistic is considered.

A bound on the probability of error is obtained for anM-ary direct-detection optical communications system consisting of an amplitude-stabilized source, a lognormal atmospheric channel, and a photocounting detector array. Equal-energy, equiprobable, orthogonal signaling, and fiat independent fading at all detectors is assumed. The result reduces to that obtained previously in the absence of fading. A comparison is made with the analogous solution for the heterodyne array receiver.

A binary optical communication system, consisting of a laser transmitter, a log-normal atmospheric channel, a photocounting detector, and a likelihood-ratio decision box has been investigated. Background radiation and dark current have been taken into account. Curves are presented for the probability of error and the mutual information for varying levels of atmospheric turbulence. It was ascertained that optical preamplification could be useful in improving system performance.