The error signal at the output of a sampling reconstruction filter caused by uncorrelated noise samples is analyzed. This error is combined with a truncation error bound for the class of "self-truncating" reconstruction filters [1] to give a system error bound for a bounded class of band-limited signals.

Abstract This paper contains the results of an exploratory study aimed at developing a model which could form the basis of a comprehensive analysis of the Air Traffic Control system. This model could be used to evaluate the effects of proposed changes in the system. The results will be presented in three parts. Part I is intended to provide an overview of the results as well as a detailed description of a traffic flow model which computes the means and variances of delays experienced by individual aircraft. Since this model requires as an input a statistical description of the arrival and departure service processes, Part II describes a model which relates these processes to more basic quantities (e.g., aircraft mix, runway configuration). Since the models which are developed represent a physical system, the question of validation arises and is also discussed in Part II. Part III of the paper considers the question of designing a (real‐time) flow control system. It is formulated as a problem of minimizing a measure of system delay subject to constraints on the allowable departure and arrival times. Illustrative results are included through‐out the paper.

Abstract This is the third and final part of a study of the analysis and control of the flow of air traffic. Part I developed a traffic flow model to compute the means and variances of delays experienced by individual aircraft. Part II was concerned with the arrival and departure processes, and with the question of model validation. In this part, we consider an approach to the problem of designing a (real‐time) flow control system. Central to the approach is the problem of minimizing a measure of system delay subject to constraints on the allowable departure and arrival times.

A method is given for obtaining a closed-form expression for the characteristic function of the average power, in aT-second interval, of a zero-mean Gaussian random process. The technique, which is constructive in nature, is applicable to the class of covariance kernels whose corresponding homogeneous Fredholm integral equations admit reduction to an equivalent linear differential system. Eigenvalue evaluations are not required.

The optimum test statistic for the detection of binary sure signals in stationary Gaussian noise takes a particularly simple form, that of a correlation integral, when the solution, denoted byq(t), of a given integral equation is well behaved(L_{2}). For the case of a rational noise spectrum, a solution of the integral equation can always be obtained if delta functions are admitted. However, it cannot be argued that the test statistic obtained by formally correlating the receiver input with aq(t)which is notL_{2}is optimum. In this paper, a rigorous derivation of the optimum test statistic for the case of exponentially correlated Gaussian noiseR(\tau) = \sigma^{2} e^{-\alpha|\tau|}is obtained. It is proved that for the correlation integral solution to yield the optimum test statistic whenq(t)is notL_{2}, it is sufficient that the binary signals have continuous third derivatives. Consideration is then given to the case where a, the bandwidth parameter of the exponentially correlated noise, is described statistically. The test statistic which is optimum in the Neyman-Pearson sense is formulated. Except for the fact that the receiver employs\alpha_{\infty}(which in general depends on the observed sample function) in place of\alpha, the operations of the optimum detector are unchanged by the uncertainty in\alpha. It is then shown that almost all sample functions can be used to yield a perfect estimate of\alpha. Using this estimate of\alpha, a test statistic equivalent to the Neyman-Pearson statistic is obtained.