If a randomly varying signal or noise is used as input, it is possible to study the input-output relations of a system, over a wide band of frequencies, by the use of power spectrum analysis. This technique has been applied to the cardiovascular system, by deliberately introducing irregularity in the pressure and flow pattern, by random electrical pacing of the heart. Examples are given of the determination, by spectral analysis in the range of 0.25 to 25 cycles/sec, of aortic and femoral arterial impedance in the dog, and also of the transmission ratio for pressure oscillations along the aorta. The results agreed satisfactorily with those obtained by the Fourier analysis of single pulses. When the time scale of the irregularities was made sufficiently great, it was possible to examine aortic impedance in the very low frequency range 0.00125 to 0.125 cycle/sec. In this range the operation of the baroreceptor reflexes became apparent.

Use of Random Excitation and Spectral Analysis in the Study of Frequency-Dependent Parameters of the Cardiovascular System

Statistical evaluation of the dynamic properties of cochlear nucleus units using stimuli modulated with pseudorandom noise.

This paper represents a survey of the recent literature in the area of process identification and parameter estimation techniques applicable to lumped-parameter, deterministic, dynamical systems. Methods reviewed include statistical estimation techniques, direct and indirect methods based on optimal control theory, functional expansion, impulse response, frequency response and a number of other specific methods. Each method is presented in a consistent format which includes an outline of the general characteristics, calculational techniques, experimental techniques, reliability estimates and applications. The overall objective is to provide a basis for comparison of the methods and a guide to particular applications which will assist the reader in selecting the best method for his specific problem Comments and additions are solicited: see page 263.

A review of process identification and parameter estimation techniques

Night-time ionospheric scintillations at the magnetic equator

Spectral analysis of electroencephalograms recorded during learning in the cat, before and after subthalamic lesions.

Two continuous chemical processes, regarded as input-output systems, were probed with stationary noise, and their frequency response characteristics estimated from spectral analyses of the input and output records. Statistical confidence bands for the estimated system gitin and phase were computed. The noises were superimposed on steady operating levels of the systems, and the analyses conducted, following Goodman [l], on the assumption that the output fluctuation in each case was the sum of a linear operation on the input fluctuation and a corrupting noise uncorrelated with the input. One process was a blending operation realized in bench scale hardware; the other was a digital computer simulation of a continuous stirred tank reactor. The blender was essentially linear; the reactor, highly nonlinear. For each process, the theoretical exact (or linearized) frequency response characteristic was computed beforehand from the appropriate differential equations for comparison with the experimental results. The...

Frequency Response From Stationary Noise: Two Case Histories

Two continuous chemical processes, regarded as input-output systems, were probed with stationary noise, and their frequency response characteristics estimated from spectral analyses of the input and output records. Statistical confidence bands for the estimated system gain and phase were computed. The noises were superimposed on steady operating levels of the systems, and the analyses conducted, following Goodman [1], on the assumption that the output fluctuation in each case was the sum of a linear operation on the input fluctuation and a corrupting noise uncorrelated with the input. One process was a blending operation realized in bench scale hardware; the other was a digital computer simulation of a continuous stirred tank reactor. The blender was essentially linear; the reactor, highly nonlinear. For each process, the theoretical exact (or linearized) frequency response characteristic was computed beforehand from the appropriate differential equations for comparison with the experimental results. The agreement between the theoretical and the experimental results was reasonably good for the linear process, but noticeably poorer for the nonlinear process, and, as might be expected, progressively poorer for the nonlinear process as the amplitude of the probing noise was increased. A reason offered for this behavior is the difficulty of ensuring, especially for nonlinear processes, that the corrupting noises in a system under study are statistically uncorrelated with the system driving forces.

B. H. Kramer

Papers

Frequency Response From Stationary Noise: Two Case Histories

Frequency Response From Stationary Noise