Biorthogonal system

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

On biorthogonal and orthonormal Clebsch–Gordan coefficients of SU(3): Analytical and algebraic approaches

Abstract: Minimal biorthogonal systems of the Clebsch–Gordan (Wigner) coefficients of SU(3)⊇U(2) are discussed as well as the dual coupled bases. The closed system of analytical expressions for the dual isofactors (reduced Wigner coefficients) and the overlaps of coupled states is obtained with the help of analytical inversion symmetry. The Regge‐type symmetry of the overlaps and the boundary orthonormal isofactors (orthogonalization coefficients) is discovered. The polynomial structure of the alternative complete algebraic systems of the orthonormal SU(3) isofactors (characterized by the null spaces, symmetries, and additional selection rules and obtained by means of the Hecht or Gram–Schmidt process) is considered. The realizations of the external ‘‘missing label’’ operators of the third and the fourth orders in the minimal coupled bases, which lead to preferable algorithms to evaluate the orthonormal SU(3) coupling coefficients satisfying different symmetry properties, are presented. With the help of the 6j coef...

Biorthogonal Wavelets on Local Fields of Positive Characteristic

Abstract: We generalize the concept of biorthogonal wavelets to a local field $K$ of positive characteristic We show that if the translates of the scaling functions of two multiresolution analyses are biorthogonal, then the associated wavelet families are also biorthogonal Under mild assumptions on the scaling functions and the wavelets, we also show that the wavelets generate Riesz bases for $L^2(K)$

Fast algorithms for orthogonal and biorthogonal modulated lapped transforms

Abstract: New algorithms for the computation of orthogonal and biorthogonal modulated lapped transforms (MLTs) are presented. The new structures are obtained by combining the MLT window operators with stages from a previously introduced structure for the type-IV discrete cosine transform (DCT-IV). The net result is fewer multiplications and additions than previously reported algorithms. For the orthogonal MLT, in particular, the new structure requires the computation of a slightly modified DCT-IV and some extra additions, but no further multiplications; so it demonstrates that the multiplicative complexity of the orthogonal MLT is the same as that of the DCT-IV.

Design of High-Performance ECG Detector for Implantable Cardiac Pacemaker Systems using Biorthogonal Wavelet Transform

Abstract: A digital electrocardiogram (ECG) detector with low power consumption and high performance based on biorthogonal 2.2 wavelet transform and applicable for the modern implantable cardiac pacemakers is proposed in the present work. Biorthogonal 2.2 wavelet transform is chosen due to its high SNR, less number of coefficients, resemblance of shape with ECG wave and ability to increase QRS complex detection performance. Architecture of the proposed ECG detector includes modified biorthogonal 2.2 wavelet filter bank and a modified soft threshold-based QRS complex detector. Three low-pass filters and one high-pass filter with pipelined architecture are used which are lesser than the earlier designed detectors. Various blocks of proposed detector are designed to denoise the input ECG signal and then to find the correct location of R-wave. Verilog hardware description language for design entry, Modelsim embedded in Xilinx ISE v.14.1 for simulation, Virtex-6 FPGAs for synthesis and Xilinx ISE tools are used to measure the performance, area and power of the proposed ECG detector and its constituent blocks. A low detection error rate of 0.13%, positive predictivity ( $$\hbox {P}^{+}$$ ) of 99.94% and sensitivity ( $$\hbox {S}_{\mathrm{e}}$$ ) of 99.92% are achieved for the proposed ECG detector which are better compared to the previous results. Also, it consumes only 20 mW of total power at 50 KHz and shows the overall delay of 18.924 ns which makes it useful for the low power and high-performance applications.