Characterization of unknown linear systems based on measured CW amplitude
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Abstract:
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.< Keywords:
Impulse response
A method is presented for predicting the total response, in both frequency and time, of an unknown linear system when only the measured continuous wave (cw) magnitude is available. The approach is based on approximating the square of the measured magnitude by a rational function, from which various system transfer functions in terms of complex frequency are deduced. These transfer functions may or may not be at minimum phase. The corresponding impulse response is then obtained by taking the inverse Laplace transform of the transfer function. The impulse response of the minimum-phase case rises faster initially to its first maximum than the nonminimum-phase counterparts. This result confirms that, for the same cw magnitude response, the accumulative energy contained in the impulse response is the greatest when the transfer function is at minimum phase. Physical meaning of the energy content is also discussed.
Impulse response
Phase response
Minimum phase
Linear phase
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Impulse responses of the piezoelectric photoacoustic (PA) signal have been measured by using the technique of cross correlation. Experimental impulse responses of aluminum model samples are in good agreement with theoretical prediction. It is shown that thermal diffusivities of opaque materials can be determined by measured zero-crossing times of PA impulse response. Cracks in aluminum samples are detected by measuring a one-dimensional image of the impulse response of the PA signal.
Impulse response
SIGNAL (programming language)
Photoacoustic effect
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For linear systems, the dynamic characteristics can be represented either by input-output data such as frequency characteristics and impulse responses or models with finite number of parameters. Previous optimal control system design has been done for parametric models such as the state space equation or transfer function. The construction of such parametric models always includes errors, so the direct design of the controller from the pulse response may avoid the concern about the modelling error. The paper presents H/sub /spl infin// output feedback controller design from the pulse response.
Impulse response
Parametric model
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Transfer function (TF) phase can be analyzed from the impulse response in a vibrating system. This letter analyzes the truncated impulse response of such a system and its phase characteristic by using a simple two-pole model. The estimated phase turns out to be highly sensitive to the window length of the truncated impulse response used for phase analysis. The minimum-phase behavior of a TF for example, is changed into a nonminimum-phase characteristic due to the truncation. An exponential window is recommended for the data analysis of vibrating systems in order to reduce the effect of truncation on the phase.
Impulse response
Impulse invariance
Truncation (statistics)
Phase response
Minimum phase
Finite impulse response
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The relations among the step response, impulse response and the transfer function of system are classical conclusions and are well_known by people engaged in control theory. In this article, some new conclusions and opinions, which can only be used in single_input_single_output control system under the premise of zero initial value, are proposed. A new general method—construction method for getting a system's transfer function from its typical response is given. The conclusions proposed are essential to the connections among the three parts and provide considerable value for teaching and science research.
Impulse response
Fuzzy Control
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The paper presents the acoustic source localization in a 2D rectangular room by using the measured acoustic impulse response. Two cases are considered: a corner of a room and a corridor. In each case, a theoretical analysis based on image source model is presented. To identify the source position, until some ambiguities, a single acoustic impulse response is required. To overcome these ambiguities, two additional impulse responses are needed. The three impulse responses can be obtained in the same time or by sequential measurements, two at a time. Experimental results obtained by real measurements which prove the theoretical ideas are presented.
Impulse response
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A technique for predicting the response of a linear system to an electromagnetic pulse, based only on the measured continuous-wave magnitude, is applied to a particular system as a case study. The measured magnitude representing the system's transfer function is deduced first from the measured response to a known CW source. We next we derive an analytic expression for the magnitude square of the transfer function to approximate the measured data and obtain a system transfer function in terms of the complex frequency. Finally, we predict the system's CW phase characteristics and its multiple solutions due to a given impulse source.
Impulse response
Closed-loop pole
Phase response
Square wave
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The transfer function of the human ear in a free sound field is measured by an impulse response technique. The impulse response of the system is determined and the frequency response is computed with aid of a digital computer. Disturbing responses in time and frequency domain caused by loudspeaker, probe microphone, and surrounding objects are eliminated.
Impulse response
Impulse invariance
Free field
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This paper proposes a method for determining transfer functions for structural systems exposed to random vibration. The technique used depends heavily upon certain properties of the time-correlation functions for its utility. It is shown that the usual errors, which are introduced into the transfer function by noise in the data, system internal noise, and data cutoff transients, can be eliminated. It is also shown that the method proposed is applicable to both open-loop and closed-loop systems, and that the use of large amounts of normal-system operating data in condensed form combine to effect economies in time and accuracies in the transfer function (impulse functions or sinusoids are usually used). A brief recount of the theory is given with 3 suggestions for laboratory technique. Laboratory results are presented.
Impulse response
Cut-off
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Impulse response
Closed-loop pole
Position (finance)
Pole–zero plot
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