A sampling theorem for nonstationary random processes (Corresp.)

The well-known sampling theorem for wide-sense stationary random processes is generalized to the class of nonstationary random processes.     

The sampling window (Corresp.)

The concept of the sampling window is introduced for the central interpolation of finite energy band-limited functions. The sampling window does not increase the rate of convergence of the truncation error series, as do various convergence factors, but does significantly reduce the truncation-error bound.     

A sampling theorem for irregularly spaced sample points (Corresp.)

Two closely related series representations for a band-limited signal of finite energy are given. They both generalize the Shannon sampling series to the case of irregularly spaced sample points. One of them is itself a sampling series, and a method is indicated for calculating its terms explicitly in certain cases.     

The problem of transmission zeros in deconvolution (Corresp.)

In the deconvolution problem, the presence of noise introduces large errors in the vicinity of the zero-crossingsomega_{i}of the system function. A simple method is presented for reducing     

Walsh function generation (Corresp.)

The problem of estimating the position of a position-modulated rectangular pulse in additive white noise is considered. The maximum likelihood estimation procedure is assumed. Bounds are derived for the probability of large estimation errors.     

Cepstrum discrimination function (Corresp.)

An expression is derived for the function that governs the discrimination by the power cepstrum against components at large time delays. The function has been found to be useful in normalizing cepstrum displays.     

First-order sampling of bandpass signals--A new approach (Corresp.)

The first-order sampling of a bandpass signal when the upper cutoff frequency is a multiple of the bandwidth is reduced to an application of the low-pass sampling theorem. In the general case, a simple band-imbedding procedure restores the positioning constraint and yields the expansion.     

A note on jackknifing kernel regression function estimators (Corresp.)

Estimation of the value of a regression function at a point of continuity using a kernel-type estimator is considered and improvements by a jackknife technique are discussed. It is seen that a so-called generalized jackknife estimator asymptotically improves upon an ordinary kernel-type estimator. However, for a fixed sample size the generalized jackknife method may inflate the mean-square error.     

A sequence of upper and lower bounds for the Q function (Corresp.)

A sequence of upper and lower bounds for theQfunction defined asQ(x)= 1/ sqrt{2 pi} int_{x}^{infty} exp[(-y^{2})/2]dyis developed. These bounds are shown to be tighter than those most commonly used.     

The cepstrum as a generalized function (Corresp.)

This correspondence investigates the possibility of defining the power or energy cepstrum as a generalized function. By applying this definition, the cepstrum can formally be computed, or a formal approximation can be achieved. The asymptotic behavior of the cepstrum is also examined.     

Comparison of generalized Q- function algorithms (Corresp.)

Several methods have been proposed for calculating the generalizedQ-functionQ_{m}(alpha, beta), but only isolated comparisons of the various techniques have been reported. The accuracy, range, and execution time of prominent methods for computing theQ-function are compared, and limitations of the algorithms are identified.     

A new method of calculating the generalized Q function (Corresp.)

A recursion relationship for the modified Bessel function is used to develop recursive formulas for functions which are expressed as a Neumann series expansion. The method is applied to devise an algorithm for calculating the generalizedQfunction. Comparisons with some alternative schemes are discussed and an error analysis is presented.     

On the equivalence of Kramer's and Shannon's sampling theorems (Corresp.)

The question of Campbell concerning the possibility of applying Shannon's sampling theorem to the same functions that can be sampled by Kramer's generalized sampling theorem is investigated and illustrated for more functions which are solutions of second-order differential equations with singular coefficients. A few definitions are introduced and some theorems are proved to show, in a more precise way, that under certain conditions the two sampling theorems are equivalent.     

A restoration method for impulsive functions (Corresp.)

A method is presented for enhancing the resolution of impulsive functions which have been degraded by a known convolutional disturbance and by the addition of white noise. An autoregressive model is employed to represent the spectrum of the ideally resolved impulsive function. The method is flexible in that it allows constraints to be incorporated into the resolution scheme. Two quite diverse examples are presented as illustration.     

A trapdoor multiple mapping (Corresp.)

A public key cryptosystem is suggested in which a message is enciphered by adding its numerical value to a sum of elements selected randomly from a publicly known knapsack, thus enabling multiple mapping of the message. Data expansion is moderate while reasonable security is maintained. Since the selected knapsack elements are message-independent, the encryption is very fast.