While the title of this paper is technically correct, it perhaps would have been better to entitle it "Curve Fitting, by Analog Simulation Methods, to Obtain the Transfer Function of a Crustacean Muscle Bundle," since this short paper is almost entirely concerned with the analog techniques used to measure the amplitude and phase response of a transfer function subjected to a sinusoidal input forcing function. If the input sinusoidal frequency is slowly swept across the frequencies of interest, then such measuring circuits (if they are fast enough) will allow the experimenter to generate a continuous Bode plot (i.e., gain and phase versus frequency) of the simulated transfer function.

A simulation of the trajectory of underwater acoustic rays is implemented on a general-purpose electronic-analog computer. Equations defining the phenomena are summarized, assumptions are listed, and a preferred form of the equations is developed to provide maximum attainable accuracy of solution. Included are considerations of the velocity of sound as an arbitrary function of both depth and range, and the effects of reflections from both the surface and an arbitrary bottom. A complete computer diagram is presented and special circuits are described. Typical results of depth versus range are shown for varying launch depths and launch angles. A method of obtaining the difference in time required for rays leaving a common emitter at various angles to reach a common receiver is also derived. By use of perturbations, Taylor series expansions, and the method of steepest descents to insert the constraint cos θ/c = constant, the overall error in this highly sensitive computation has been reduced to 0.01 per cent or better.

It is shown in this paper how a straightforward solution to the regression problem can be obtained for continuous variables on a general-purpose analog computer. The linear case (least squares straight line) is thoroughly described. A specific nonlinear problem, that of estimating the parameters of a missile trajectory, is also described. The regression equations are derived and analog computer circuits for the solution are drawn. It is also shown that the steepest descent technique for parameter optimization is essentially the same technique as the classical statistical methods of multivariate regression analysis, but that significant analog computer circuit simplification occurs in using the steepest descent technique applied directly to the objective function.

One method of searching a system for optimum operating conditions is to evaluate system performance for many randomly-chosen combinations of the independent parameters. This paper explains the use of standard electronic analog computer equipment to accomplish such a search of a mathematical model quickly and economically. Gaussian noise sources generate values of the independent parameters and sample-hold circuits hold those values which give the best value of the optimization criterion. An application of the method to a production allocation problem is mentioned.