Biorthogonal system

About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.

Design of wavelet transform based electrocardiogram monitoring system.

Abstract: The new age advancements in information technology due to materials and integrated circuit (IC) technologies and their applications in biomedical sciences have made the healthcare facilities more compact and affordable for the aging population. Market trends in healthcare and related devices indicate a sharp rise in their demand. Hence the researchers have converged the efforts on designing more smart and advanced medical devices using IC technology. Among these devices, cardiac pacemakers have become a recurrent biomedical device which is engrafted in the human body to detect and monitor a person's heart beating rate. The data thus generated is processed for various medical usages and devices via wireless methods. Cardiovascular diseases (CVDs) or diseases related to the heart are due to abnormalities or disorders of the heart and blood vessels. Till date, limited literature is available which focuses on a single technique that can perform all of the ECG signal denoising, ECG detection, lossless data compression and wireless transmission. In this work, a joint approach for denoising, detection, compression, and wireless transmission of ECG signal is proposed. The modified biorthogonal wavelet transform is used for denoising, detection and lossless compression of ECG signal. To reduce the circuit complexity, biorthogonal wavelet transform is realized using linear phase structure. Further, it is found in this work that the usage of modified biorthogonal wavelet transform increases the detection accuracy and CR of the proposed design. Also, in this work, the Wi-Fi-based wireless protocol is used for compressed data transmission. The proposed ECG detector achieves the highest sensitivity and positive predictivity of 99.95% and 99.92%, respectively, with the MIT-BIH arrhythmia database. The use of modified biorthogonal 3.1 wavelet transform and run-length encoding (RLE) for the compression of ECG data achieves a higher compression ratio (CR) of 6.271. To justify the effectiveness of the proposed algorithm, which uses modified biorthogonal wavelet 3.1transform, the results are compared with the existing methods, namely, Huffman coding/simple predictor, Huffman coding/adaptive, and slope predictor/fixed length packaging.

Representation of Functions by Generalized Dirichlet Series

Abstract: This article is concerned with the representation of functions in domains of the complex plain by series in the systems , , .In § 1 we construct systems biorthogonal to the systems , , and find the asymptotic behaviour of functions of these systems.In § 2 we determine in a natural way the coefficients of the series in the systems in question by means of the biorthogonal systems. We also find the asymptotic behaviour of the coefficients for large indices. We obtain formulae for the remainder, that is, the difference between the function and a partial sum of the corresponding series.In § 3 we prove that a function whose coefficients in the series are all zero must itself be zero. This result makes it possible, in principle, to reconstruct a function from the coefficients of its series.In § 4 we give conditions under which the series, or a subsequence of its partial sums, converges to the corresponding function.

An abstract framework for a priori estimates for contact problems in 3D with quadratic finite elements

Abstract: In this paper, a variationally consistent contact formulation is considered and we provide an abstract framework for the a priori error analysis in the special case of frictionless contact and small deformations. Special emphasis is put on quadratic mortar finite element methods. It is shown that under quite weak assumptions on the Lagrange multiplier space $${\mathcal{O} (h^{t-1}), 2 < t < \frac52}$$ , a priori results in the H 1-norm for the error in the displacement and in the H ?1/2-norm for the error in the surface traction can be established provided that the solution is regular enough. We discuss several choices of Lagrange multipliers ranging from the standard lowest order conforming finite elements to locally defined biorthogonal basis functions. The crucial property for the analysis is that the basis functions have a local positive mean value. Numerical results are exemplarily presented for one particular choice of biorthogonal (i.e. dual) basis functions and also comprise the case of finite deformation contact.

Construction of multivariate biorthogonal wavelets with arbitrary vanishing moments

Abstract: We present a concrete method to build discrete biorthogonal systems such that the wavelet filters have any number of vanishing moments. Several algorithms are proposed to construct multivariate biorthogonal wavelets with any general dilation matrix and arbitrary order of vanishing moments. Examples are provided to illustrate the general theory and the advantages of the algorithms.