An interactive technique for statistical tolerance analysis has been developed for a computer with graphic display. The computer program called TAP provides for random perturbation of parameter values, repeated evaluation of system performance, and display of distribution histograms. The interactive capability of the program enables the designer to introduce modifications to the system so that the relative effects of these changes can be quickly evaluated with the graphic display. The program has been implemented on a computer facility consisting of a CDC 3300 digital computer, an ITT digital display scope, and an EAI 8800 analog computer. Two applications are discussed to illustrate the adaptability of the technique to either linear or nonlinear problems. The digital simulation of an active circuit is used to show how the interaction with graphic display saves time in evaluating alternative designs. A hybrid simulation of an equalizer for a digital transmission system illustrates that complex time domain problems can be economically analyzed using TAP. In addition, it is shown how TAP is used to measure the reproducibility of an analog simulation.

The advent of iterative analog computers has greatly increased the class of problems that can efficiently be simulated with a hybrid system. The iterative analog computer has placed wide bandwidth analog components under the control of high-speed digital logic. This enables one both to increase the sophistication of the control used for the analog components and to acquire statistically significant samples of the process in a reasonable period of time. An iterative analog computer has been used to investigate methods of increasing the efficiency of signal representation systems by combining analog measurements with digital control and storage. A hybrid system has been developed that is capable of adjusting the exponential basis as well as the coefficients of the representation to minimize the integrated squared error between a signal and its representative. Since the efficiency of the representation depends upon the sampling instant chosen for measurement of the coefficients, methods of detecting this instant were investigated. A detection system has been developed that can adaptively adjust its parameters to correspond to the signal that is being processed. The data presented illustrates the dynamic accuracy of the iterative analog computer, the convergence properties of the optimization procedure, and the statistical properties of the detector when noise is present.