Perturbation size and harmonic limitations in affine approximation for time invariant periodicity preservation systems

2015

IET Computer Vision

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Both Shannon and Kolmogorov-Chaitin-Solomonoff (KCS) information models fail to measure meaningful information in images. Pictures of a cow and correlated noise can both have the same Shannon and KCS information, but only the image of the cow has meaning. The application of 'algorithmic specified complexity' (ASC) to the problem of distinguishing random images, simple images and content-filled images is explored. ASC is a model for measuring meaning using conditional KCS complexity. The ASC of various images given a context of a library of related images is calculated. The 'portable network graphic' (PNG) file format's compression is used to account for typical redundancies found in images. Images which containing content can thereby be distinguished from those containing simply redundancies, meaningless or random noise.

Section: Measuring Meaning In Imagesmentioning

confidence: 99%

Measuring meaningful information in images: algorithmic specified complexity

Ewert

Dembski

2015

IET Computer Vision

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“…The accuracy of HCW's in assessing PP systems has been perfomed on a number of test cases [33]. A overarching theoretical measure of the extent to which the HCW approximation is accurate can be estimated by deviation from a second order fit at the operating point.…”

Section: Estimation Of the Hessianmentioning

confidence: 99%

Evaluation of Harmonic Coupling Weights in Nonlinear Periodicity Preservation Systems

Baylis

IEEE Trans. Circuits Syst. I

2012

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When stimulated by a periodic stimulus, every component of a possibly nonlinear periodicity preservation system oscillates periodically with the same period as the stimulus. Changes in the harmonic structure of the the stimulus couples each input harmonic to, in general, every response harmonic. Knowledge of harmonic coupling weights (HCWs) allows model free characterization of effects of all small stimulus perturbation. This paper develops foundational methodology for experimentally measuring the HCWs. The on-frequency method uses small tickle tones at harmonic frequencies to do this. The off-frequency method places tickle tones adjacent to harmonic frequencies and is applicable to PP systems that are locally frequency invariant. Memoryless nonlinear PP systems are an example where the approach works exactly. The off-frequency method also requires fewer experiments. In some cases, the off-frequency method can be extended to measure numerous HCWs in a single experiment. Some system types such as the memoryless nonlinearity, require fewer experiments than general PP systems. Methods to experimentally measure the Hessian are also presented.

“…perturbations at multiple harmonics, a technique herein labeled frequency multiplexing of tickle tones. This can significantly reduce the number of measurement iterations necessary to fully determine the matrix of nonlinear network parameters.We examine the frequency multiplexing approach for periodicity preservation (PP) systems approach in finding the derivatives composing the system Jacobian in the Fourier series coefficient domain.The PP and time-invariant periodicity preservation (TIPP) systems have been introduced in a recently authored paper in process of publication [8], and the limitations of use on some nonlinear systems examined quantitatively in [9]. This theory forms the foundation for experimental nonlinear network analysis.…”

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confidence: 99%

“…The PP and time-invariant periodicity preservation (TIPP) systems have been introduced in a recently authored paper in process of publication [8], and the limitations of use on some nonlinear systems examined quantitatively in [9]. This theory forms the foundation for experimental nonlinear network analysis.…”

mentioning

confidence: 99%

Frequency multiplexing tickle tones to determine harmonic coupling weights in nonlinear systems

Baylis

78th ARFTG Microwave Measurement Conference

2011

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Obtaining the Jacobian parameters for a nonlinear system, such as in X-parameter or S-function measurement, requires excitation of tickle tones either on or slightly off of the main harmonic frequencies. Traditional off-frequency measurements involve simultaneous excitation with tickle tones both slightly above and/or below a single harmonic frequency at a time. This paper describes a multiplexing technique for the excitation of the system with perturbations at all harmonics simultaneously. This technique requires both frequency and cross-frequency noninterference for successful results from the measurements. If these conditions exist for the nonlinear system, the off-frequency multiplexing technique for tickle tones can reduce the measurements necessary to find the Jacobian matrices by a factor equal to the number of harmonics considered in the polyharmonic distortion. These methods provide exact results for memoryless polynomial nonlinearities.In making nonlinear network parameter measurements, such as the X-parameters 1 [1] and the S-functions [2-4], it is necessary to apply a large-signal "operating" condition, followed by small perturbations to this condition known as "tickle" tones. The authors of this paper recently have written a survey paper on nonlinear network parameters that briefly describes measurement options from a practical stance [5]. Two options exist for the tickle-tone measurements: (1) onfrequency tickle tones, where the perturbation is added at the same frequency as the desired stimulus harmonic and (2) offfrequency tickle tones [6], where the perturbation is added at a slightly offset frequency from the appropriate fundamental or harmonic. The excitation approaches have been significantly considered by Betts in recent publication [7]. While a significant percentage of modern nonlinear network analyzers use the on-frequency method, an advantage of the offfrequency method is that the results of the tickle-tone perturbations can be isolated away from large signals overlapping in frequency.This paper demonstrates that the off-frequency technique can be extended to allow simultaneous application of 1 X-parameters is a registered trademark of Agilent Technologies. perturbations at multiple harmonics, a technique herein labeled frequency multiplexing of tickle tones. This can significantly reduce the number of measurement iterations necessary to fully determine the matrix of nonlinear network parameters.We examine the frequency multiplexing approach for periodicity preservation (PP) systems approach in finding the derivatives composing the system Jacobian in the Fourier series coefficient domain.The PP and time-invariant periodicity preservation (TIPP) systems have been introduced in a recently authored paper in process of publication [8], and the limitations of use on some nonlinear systems examined quantitatively in [9]. This theory forms the foundation for experimental nonlinear network analysis.A basic discussion of the system theory describing the context of this measurement is useful. A mor...