Showing papers on "Volterra series published in 1969"
TL;DR: In this article, a nonlinear frequency-dependent model for the transistor and with Volterra series as an analysis tool was used to determine the optimum cascade that has high gain and good modulation performance especially for higher frequencies.
Abstract: Intermodulation distortion performance of cascaded transistors is analyzed using a nonlinear frequency-dependent model for the transistor and with Volterra series as an analysis tool. The objective of this study is to determine the optimum cascade that has high gain and good modulation performance especially for higher frequencies. A particular application is in long-haul, analog, solid-state coaxial systems where intermodulation distortion is a critical problem. Both experimental as well as computer results are used in this analysis. It is shown, for example, that certain low distortion configurations can exhibit high distortion when cascaded. A few optimum cascade configurations are discussed in detail.
45 citations
01 Oct 1969
TL;DR: In this article, the authors derived a formula for the distortion-noise power in frequency-dependent nonlinear networks represented by a Volterra series for transistor feedback amplifiers and f.m. radio-relay amplifiers.
Abstract: Formulas are derived for the computation of distortion-noise power in frequency-dependent nonlinear networks represented by a Volterra series. The integrals for the distortion-power spectrum contain higher-dimensional Laplace transforms of the corresponding kernels of the Volterra series. An analysis of the frequency-dependent nonlinearity is carried out for transistor feedback amplifiers and f.m. radio-relay amplifiers used in frequency-division-multiplex transmission systems. The nonlinearity of a given order for transistor feedback amplifiers is characterised by a distortion term, and its frequency characteristic, which can be computed or determined from certain intermodulation measurements. A linear f.m. amplifier is completely characterised by its transfer immittance W12 (jω).
12 citations
01 Nov 1969
8 citations
TL;DR: In this article, two methods of evaluating a Volterra series have been used in the literature using contraction mapping theorems, these two methods are shown to give identical series and an algorithm is developed for evaluating the series.
Abstract: Two methods of evaluating a Volterra series have been used in the literature Using contraction mapping theorems, these two methods are shown to give identical series An algorithm is developed for evaluating the series
7 citations
TL;DR: In this article, the authors present necessary and sufficient conditions for the existence of an optimal control for a class of nonlinear systems described by an infinite series of Volterra type. But their results are limited to linear and nonlinear stationary and time-varying systems.
Abstract: This paper presents necessary and sufficient conditions for the existence of an optimal control for a class of nonlinear systems described by an infinite series of Volterra type. Variational methods are applied to minimize quadratic cost functionals leading to a class of nonlinear integral equations. Sufficient conditions for the existence and uniqueness of a solution of this integral equation are presented using abstract analysis. To the best knowledge of the author these results are new. The technique presented here applies to linear and nonlinear stationary and time-varying systems described by input-output functional relations through finite or infinite Volterra series. An example of nonlinear systems described by an infinite series of Volterra type is presented for illustration.
6 citations
01 Jan 1969
TL;DR: In this paper, a sufficient condition for the boundedness of the response of a nuclear power reactor to an arbitrary, constantly acting, bounded input was determined. But the conditions on the initial conditions of the system were not taken into consideration.
Abstract: Barrett has recently suggested the use of the majorant of a Volterra series for the determination of the system-response bounds. This reduces a nonlinear differential equation to an ordinary algebraic equation, thus considerably facilitating the study of the convergence properties of a Volterra-series expansion. The author has applied this method to a practical problem to investigate the effect of temperature-feedback control on the growth of neutrons in a nuclear-power reactor. This paper determines a sufficient condition for the boundedness of the response of the nuclear reactor subjected to an arbitrary, constantly acting, bounded input. The nonzero initial conditions of the system have been taken into consideration, and their effects on the system response are clearly shown.
4 citations
TL;DR: It is shown that the sampled output of a nonlinear system with sampled-data input is given by the discrete equivalent of a Volterra series in which the kernels are the sampledVolterra kernels of the system.
Abstract: It is shown that the sampled output of a nonlinear system with sampled-data input is given by the discrete equivalent of a Volterra series in which the kernels are the sampled Volterra kernels of the system. This theorem is then extended to the common case in which the sampled-data input is applied to the nonlinear system through a zero-order hold.
4 citations
Dissertation•
01 Jan 1969
TL;DR: In this paper, the problem of estimating the kernels of time-invariant multivariable and nonlinear dynamical systems, using periodic-step-sequence inputs of the pseudorandom type, has been studied.
Abstract: The thesis deals with theoretical aspects of the measurement, by correlation, of the kernels of time-invariant multivariable and nonlinear dynamical systems, using periodic-step-sequence inputs of the pseudorandom type. The crosscorrelation of equal-length pairs of binary maximum-length sequences is examined in detail. The frequency distributions of the correlation coefficients are listed for all such pairs of period < 255, and formulae are derived for the first four moments of the distribution. A limited amount of information about the correlation sequences is obtained from a study of the generating polynomials. The sampling property of maximum-length sequences is used, in an alternative approach, to classify the frequency distributions. Finally, recent work by Gold (1968) is related to the author's work on ternary correlation sequences, and suggestions are made for extending this. The problem of calculating the linear kernels of a multi-input system, from input/output crosscorrelations evaluated at sample time intervals, is found to reduce to the solution of a finite set of linear algebraic equations in the system 'weights'. Two cases of practical importance are found to yield exactly N independent equations, where N is the period of the output signal. From this result, and a review of other work, a suggestion is made as to the best type of input for any multiple linear identification. The same reduction to N equations is found to hold for a singleinput nonlinear system, defined by a Volterra series of any order, when the test signal is a binary or inverted-binary maximum-length sequence, or a ternary maximura-length sequence. A non-rigorous argument is adduced to show why this reduction to N equations may hold for any form of identification by sample-interval correlation using synchronized periodic step sequences. It is proved that all binary maximum-length sequences, but not all ternary sequences, can be started at such a point that the first moment vanishes.