Frequency Response From Stationary Noise: Two Case Histories
TL;DR: In this paper, 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.
Abstract: 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...
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TL;DR: 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, and the results agreed satisfactorily with those obtained by the Fourier analysis of single pulses.
Abstract: 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.
124 citations
TL;DR: The responses of single units in the cochlear nucleus of the rat can be described using linear system theory when the modulation depth is kept low, and the advantages of using random noise signals in studies of the dynamic properties compared with sinusoidal modulation signals are discussed.
70 citations
TL;DR: A survey of the recent literature in the area of process identification and parameter estimation techniques applicable to lumped-parameter, deterministic, dynamical systems and a guide to particular applications which will assist the reader in selecting the best method for his specific problem.
Abstract: 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.
65 citations
TL;DR: In this paper, the nocturnal and seasonal variations of equatorial ionospheric scintillations are presented and classified into two classes, namely, class I and class II depending on their fading rates and association with bottomside spread-F.
54 citations
TL;DR: A specific stochastic model of the approach waves in these structures is proposed, which suggests that any irregular activity in these two areas is unshared between them, and any regular activity is shared.
47 citations
References
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Book•
01 Jan 1958
TL;DR: The aim of this book is to clarify the role of noise in the development of linear and nonlinear systems and to provide a procedure forormalising the noise generated by these systems.
Abstract: Preface to the IEEE Press Edition. Preface. Errata. Introduction. Probability. Random Variables and Probability Distributions. Averages. Sampling. Spectral Analysis. Shot Noise. The Gaussian Process. Linear Systems. Noise Figures. Optimum Linear Systems. Nonlinear Devices: The Direct Method. Nonlinear Devices: The Transform Method. Statistical Detection Signals. Appendix 1: The Impulse Function. Appendix 2: Integral Equations. Bibliography. Index.
1,473 citations
Book•
14 Jul 2012
TL;DR: This account attempts to provide and relate the necessary ideas and techniques in reasonable detail to develop the insight necessary to plan both the acquisition of adequate data and sound procedures for its reduction to meaningful estimates.
Abstract: The measurement of power spectra is a problem of steadily increasing importance which appears to some to be primarily a problem in statistical estimation. Others may see it as a problem of instrumentation, recording and analysis which vitally involves the ideas of transmission theory. Actually, ideas and techniques from both fields are needed. When they are combined, they provide a basis for developing the insight necessary (i) to plan both the acquisition of adequate data and sound procedures for its reduction to meaningful estimates and (ii) to interpret these estimates correctly and usefully. This account attempts to provide and relate the necessary ideas and techniques in reasonable detail — Part I of this article appeared in the January, 1958 issue of THE BELL SYSTEM TECHNICAL JOURNAL.
1,353 citations
TL;DR: In this article, a well-agitated continuous reactor either of the liquid or fluidized variety is considered under various types of control and criteria are derived enabling one to determine under what conditions different modes of control are successful.
349 citations