The characteristic function and the probability density of a pulse train at the output of a linear system
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This paper presents a method to translate pulse-amplitude modulated discrete controls, for which many design algorithms exist, into pulse-width modulated controls extensively used in aerospace applications. Assuming that a discrete control law is available for a linear time-invariant multivariable system, the conditions for an approximate equivalent pulse-width application of the inputs are developed. The approximation is based on pulse, i.e., amplitude • duration, intensity equivalence, and on the evaluation of an optimum firing delay that maintains, independently from the control and external input, the dynamic performances of the system, including stability. A simple numerical example on a second-order system points out the benefits and drawbacks of the method, which is then applied to a typical complex aerospace design problem, i.e., shape and pointing control of a space antenna.
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This paper presents a new time domain technique for computing the noise spectral density. The power spectral density is interpreted as the asymptotic value of the expected energy spectral density per unit time. We show that the methodology of stochastic differential equations can be used to derive a set of ordinary differential equations for the expected energy spectral density. This set of equations can then be integrated in time until the steady state value of the power spectral density is obtained. The method is quite general and can be used to find the noise spectrum in any circuit in which noise can be treated as a perturbation. In this paper, the algorithm has been used to simulate the spectrum of the noise voltage in switched capacitor circuits.
Noise spectral density
Switched capacitor
Noise power
Noise temperature
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Results are reported on the attempt to define a pseudotransfer funtion of a circuit composed of a 2-pulse canceler and hard limiter.
Limiter
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We constructed an analog circuit generating fluctuations of which a probability density function has power law tails. In the circuit, fluctuations with an arbitrary exponent of the power law can be obtained by tuning the resistance. A theory of a differential equation with both multiplicative and additive noises which describes the circuit is introduced. The circuit is composed of a noise generator, an analog multiplier and an integration circuit. Sequential outputs of the circuit are observed and their probability density function and autocorrelation coefficients are shown. It is found that correlation time of the autocorrelation coefficient is dependent on the power law exponent.
Electrical network
Electric generator
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An n-bit binary signal is considered to be a vector in an n-dimensional Euclid space. Based on the real number obtained by taking an inner product of the vectors in this space, a signal of normal density distribution will be generated.
SIGNAL (programming language)
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A simple method known in network theory is used to determine the complete characteristics of an unknown linear system from a given CW (continuous wave) magnitude response only. These characteristics include possible different transfer functions, their phases, and the corresponding impulse responses. Only one transfer function has minimum phase. The main achievement is to deduce an approximate squared-magnitude function in the form of a ratio of two even polynomials based on the outstanding features, such as resonant frequencies and bandwidths, contained in the given measured magnitude. The remaining procedures for obtaining the complete system characteristics are exact. It is also shown that the minimum-phase case, through its associated impulse response and accumulated energy content, constitutes the most conservative estimate for the initial threat to the system by an external unfriendly source.< >
Impulse response
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A realization of a variable frequency RC oscillator, using the concept of frequency-dependent negative conductance, is proposed, The frequency variation is obtained by controlling a single resistance in the network.
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Chapter 8 establishes the relationship between the input and output power spectral densities of a linear system. Limitations on results are carefully detailed and the case of oscillator noise is considered. The theory is extended to multiple input–multiple output systems.
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General relations for the energy spectral densities of nonperiodic signals constrained in bandwidth in nonlinear reactances are derived. It is assumed that the charge-voltage characteristics of the reactances are polynomials. In addition certain conditions for the frequency bands of the signals must be met. By contrast with the Manley-Rowe relations integrals with respect to frequency appear instead of the ratios power over frequency. The integrands are energy spectral densities divided by frequency. For parametric devices inequalities can be derived for the ratios of the energy levels in the different circuits and the limiting frequencies of the energy spectral densities. With these inequalities it is possible to determine limits for the energy levels.
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