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The notable increase in the size and dimensions of data have presented challenges for data storage and retrieval. The Bloom filter and its generations, due to efficient space overheads and constant query delays, have been broadly applied to querying memberships of a big data set. However, the Bloom filter and most of the variants regard each element as a 1-dimensional string and adopt multiple different string hashes to project the data. The interesting problem is when the inputs are numerical vectors with high dimensions, it remains unknown whether they can be projected into the Bloom filter in their original format. Furthermore, we investigate whether the projection is random and uniform. To address these problems, this paper presents a new uniform Prime-HD-BKDERhash family and a new Bloom filter (P-HDBF) to retrieve the membership of a big data set with the numerical high dimensions. Since the randomness and uniformity of data mapping determines the performance of the Bloom filter, to verify these properties, we first introduce information entropy. Our theoretical and experimental results show that the P-HDBF can randomly and uniformly map the data in their native formats. Moreover, the P-HDBF provides an efficient solution alternative to implement membership search with space-time overheads. This advantage may be suitable for engineering applications that are resource-constrained or identification of the nuances of the graphics and images. [ABSTRACT FROM AUTHOR]

The paper tries to apply the Butterworth low-pass filter to inertial navigation system (INS) data processing. A set of INS heading data of a practical example has been calculated and the filtering tested. This filtering method is used to examine the correction of the results made by Guo and Wang. Based on the discrete Fourier transformation and the digital filter design technique, a Butterworth low-pass digital filter has been designed and performed to process INS heading raw data. The design of a special Butterworth filter includes determination of the technical specification of the filter and of the response function in the time domain or the frequency domain (determination of the order and cutoff frequency of the digital filter). For the high-frequency noise of INS raw data, a Butterworth low-pass filter has been designed to obtain a more accurate INS heading. The choice of the parameters and orders of the filter is also discussed in the paper. Finally, an example of INS heading data calculation is presented. The signal-processing TOOLBOX of MATLAB software is used for calculating and mapping the results. The result (RMS) is at the level of 0.01°. The method described here is simpler than Kalman filtering or the smoothing method and has sufficient accuracy for INS processing. It also provides ideas for some other series of raw data with high-frequency noise. [ABSTRACT FROM AUTHOR]

This paper considers the complex coefficient transfer function with transmission zeros on the imaginary axis and presents a method to realize such a transfer function by a reactance network including imaginary resistors with double resistor termination. Using the obtained network and the reference network for the complex-wave digital filter, the complex digital filter with transmission zeros on the imaginary axis can easily be extended, which is important in practice. In this paper, Brune's method modified by Belevitch as well as Fujisawa's method extended by Morimoto et. al. are improved and the realizability condition is relaxed. Then, several construction examples are shown an the features of construction methods are compared and discussed. [ABSTRACT FROM AUTHOR]

This paper studies the chaotic oscillations in a dissipative system generated by a second-order direct-form II digital filter with a 2's complement adder. The locus of this chaotic oscillation is absorbed into the parallel lines comprising the Cantor-like set on the state space. In this paper, with respect to the chaotic oscillation, the initial value dependence of the locus, the output distribution, and the fractal dimensions of the locus on the state space are investigated as the fundamental nature of the chaos. Also, by considering this filter as the two-dimensional mapping, the mechanism generating the Cantor-like attractor is studied. From this study, it is shown that the 2's complement adder characteristic has functions for stretching and folding of the state space causing the chaos. Also, the coefficient dependence of the Cantor-like attractor is studied and the relationship between the fractal dimensions of the locus and the coefficient are presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of filter design for linear continuous-time systems with arbitrarily fast time-varying parameters is investigated. The time-varying parameters belong to a polytope with known vertices, affect all the system matrices and are assumed to be available online for implementation of the filters. Necessary and sufficient parameter-dependent linear matrix inequality (LMI) conditions for the existence of a parameter-dependent filter assuring that the estimation error dynamics is quadratically stable and satisfies bounds to the or to the norms are given. A sequence of standard LMI conditions assuring the existence of homogeneous polynomially parameter-dependent (HPPD) solutions to the parameter-dependent LMIs for filter design is provided in terms of the vertices of the polytope (no gridding is required), yielding parameter-dependent filters of arbitrary degree assuring quadratic stability of the error dynamics for the or the cases. As the degree of the HPPD solutions increases, less and less conservative LMI conditions are obtained, tending to the necessary conditions that assure optimal values for the or the performance of the estimation error dynamics under quadratic stability. Numerical examples illustrate the results, showing that parameter-dependent filters can provide better attenuation levels than the ones obtained with robust filters, at the price of a more complex filtering strategy. [Copyright &y& Elsevier]

The paper deals with the problem of best mean-square interpolation of a continuous q-variate weakly stationary random process x over R on the basis of the values xκ, κ κ ϵ Z, which was studied first by A. M. Yaglom [Uspehi Matem. Nauk (N.S.), 4 (1949), pp. 173-178 (in Russian)] in the case q = 1. For the family JZ of all subsets of R which are shifts of Z, criterions of JZ-singularity and JZ-regularity in terms of the nonstochastic spectral measure of x are given. Related results for stationary sequences over Z are stated. [ABSTRACT FROM AUTHOR]

The paper presents results of local performance analysis of a generalized adaptive notch filter (GANF). GANFs are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. The tracking properties of the algorithm are studied analytically using a direct averaging approach and an approximating linear filter technique. Even though restricted to a single-frequency case, the presented analysis provides valuable insights into the tracking mechanisms of GANF, including the associated speed/accuracy tradeoffs, the achievable performance bounds, and tracking limitations. In addition, it allows one to formulate some useful rules of thumb for choosing design parameters. [ABSTRACT FROM AUTHOR]

We show that the existence of two incomparable selective ultrafilters imply the existence of two groups H and G such that for every cardinal κ, Hκ and Gκ are countably compact but H×G is not countably compact. In other words, the existence of two incomparable selective ultrafilters shows that the Comfort group order is not downward directed, answering in the affirmative Question 482 posed by Garcia-Ferreira in the paper of Comfort in the Open Problems in Topology. [Copyright &y& Elsevier]

This paper presents a time-delayed impulsive feedback approach to the problem of stabilization of periodic orbits in chaotic hybrid systems. The rigorous stability analysis of the proposed method is given. Using the time-delayed impulsive feedback method, we analyze the problem of detecting various periodic orbits in a special class of hybrid system, a switched arrival system, which is a prototype model of many manufacturing systems and computer systems where a large amount of work is processed in a unit time. We also consider the problem of stabilization of periodic orbits of chaotic piecewise affine systems, especially Chua's circuit, which is another important special class of hybrid systems. [ABSTRACT FROM AUTHOR]

The objective of this paper is to develop an approach to nonlinear filtering which allows the separation of time-consuming computations involving the coefficients of the system from those dealing with the observation data only. The approach is based on a Cameron-Martin type expansion for nonnormalized optimal filters. [ABSTRACT FROM AUTHOR]

This paper presents a new method for designing orthonormal wavelet filter banks using the Remez exchange algorithm. It is well known that orthonormal wavelet bases can be generated by paraunitary filter banks. Thus, synthesis of orthonormal wavelet bases can be reduced to the design of paraunitary filter banks. From the orthonormality and regularity of wavelets, we derive some conditions that must be satisfied for FIR paraunitary filter banks, and investigate the relationship between the filter coefficients and their zeros. According to the relationship, we apply the Remez exchange algorithm in the z-domain directly and formulate the design problem in the form of a linear problem. Therefore, we can easily get a set of filter coefficients by solving the linear equations. Optimal solutions with an arbitrary regularity can be obtained after using an iteration procedure. In the proposed method, the main advantage is that less computational complexity is required as compared with the conventional methods. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(6): 1–8, 1998 [ABSTRACT FROM AUTHOR]

This paper discusses error spectrum shaping for 2D state-space digital filters. In order to reduce cost by reducing the total number of parameters, a method of analytic design is proposed in which the error feedback coefficient is specified by a diagonal matrix. The proposed algorithm has the feature that the optimal error feedback coefficient can be designed analytically in closed form by minimizing a quadratic form. The validity of the proposed algorithm is demonstrated with a numerical example. The noise reduction effect where the subdecimal part of the optimal coefficient is rounded by the power of 2 is also demonstrated. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 79–90, 1998 [ABSTRACT FROM AUTHOR]

This paper proposes a method of realizing arbitrary complex coefficient transfer functions with complex double resistively terminated lossless filters as the reference network for complex wave digital filters (CWDFs). For this purpose, the Darlington synthesis method, which is known for realizing arbitrary real coefficient transfer functions, is expanded into the complex domain. Furthermore, a new construction method for a digital adapter without a delay-free loop is presented. Finally, a complex coefficient transfer function using some realization method is constructed and the validity of the proposed method is confirmed. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(2): 12–23, 1997 [ABSTRACT FROM AUTHOR]

This paper proposes the optimal design for the separable-denominator two-dimensional digital filter, using the genetic algorithm (GA). The design proposed is for the specification in the frequency domain. The simple GA, which is the most basic among GA, is used in the proposed optimal design. The parameters of the transfer function of the separable-denominator two-dimensional digital filter are encoded into bit sequences, and then GA is applied to design the filter. By the use of the separable-denominator transfer function, the stability of the filter is completely guaranteed. The approximation error of the proposed method is compared to that of the conventional method through design examples. The convergence of GA is discussed. It is shown that the proposed optimal design can easily cope with the modification of the design specification of the two-dimensional digital filter. It is shown also that the filter can be designer using the maximum error or the absolute error sum as the error evaluation function in addition to the mean-square error. [ABSTRACT FROM AUTHOR]

This paper presents a design and implementation method for the linear phase two-channel perfect reconstruction finite impulse response (FIR) filter banks with arbitrary filter lengths. This method is labeled a weighted Lagrange-Newton method; it is obtained by introducing the least squares weighting function into the Lagrange-Newton method. Filter banks with good stopband attenuation (equiripple stopband) can be designed using this method. Furthermore, a new method is presented that makes the filter banks with a lattice structure using the property of a polyphase component matrix. The filter banks can achieve perfect reconstruction in spite of coefficient quantization. [ABSTRACT FROM AUTHOR]

During the past few years, there been a series of paper published on the theory of the natural observation method. As one of the important application of this theory, the problems of acceptance and generation of a general waveform are discusses here. The case of polynomial waveforms and its corresponding theory was published previously. A great extension of the theory which general waveforms is presented here and its full picture is clarified. [ABSTRACT FROM AUTHOR]

This paper considers the design of transmitter and receiver FIR digital filters with partial response of class II and V for data transmission, The filters are required to band-limit the transmitting and receiving signal, while maintaining the overall impulse response with zero intersymbol interference (ISI). Two cases are considered: 1) the case where the transmitter itself has the zero ISI impulse response; and 2) the case where the transmitter and receiver filters are matched. In the former, the length of the filter is set to be equal to the number of samples between two zero-cross points, which are at a certain symmetrical distance from the center of the ideal impulse response. Then a linear-phase transfer function is derived with an equiripple approximation to the ideal amplitude frequency response. In the approxiamtion, the weight in the stopband is set as less than 1, and ISI of less than 1 percent is obtained. In the design of the matched filter pair, the overall order is set in the same way as in the former. Applying the Herrman-Schuessler design method for the minimum phase-shift filter in the frequency domain, the transfer function is derived. To realize ISI of less than 1 percent, it suffices to set the weight in the stopband less than 5 times in the passband. Although an effort was made to decrease ISI by successive approximation with the mirror zeros as the parameters, only a slight improvement was obtained. In either case, class V requires approximately a twice higher order than class II to realize the same attenuation and ISI. [ABSTRACT FROM AUTHOR]