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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 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]

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]