Biorthogonal system

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

MINLAB: minimum noise structure for ladder-based biorthogonal filter banks

Abstract: We introduce a minimum noise structure for ladder-based biorthogonal (MINLAB) filter bank. The minimum noise structure ensures that the quantization error has a unity noise gain, even though the filter bank is biorthogonal. The coder has a very low design and implementation cost. The perfect reconstruction property is structurally preserved. Optimal bit allocation and coding gain formulas are derived. We show that the coding gain of the optimal MINLAB coder is always greater than or equal to unity. For both AR(1) process and MA(1) process, the MINLAB coder with two taps has a higher coding gain than the optimal orthonormal coder with an infinite number of taps. In addition to its superior decorrelation ability, it has many other desired features that make it a potentially valuable and attractive alternative to the orthonormal coder, especially for a high-fidelity compression.

Topological phase transitions driven by non-Hermiticity in quantum spin Hall insulators

Abstract: The interplay between non-Hermiticity and topology opens an exciting avenue for engineering novel topological matter with unprecedented properties. While previous studies have mainly focused on one-dimensional systems or Chern insulators, here we investigate topological phase transitions to and from quantum spin Hall (QSH) insulators driven by non-Hermiticity. We show that a trivial to QSH insulator phase transition can be induced by solely varying non-Hermitian terms, and there exists exceptional edge arcs in QSH phases. We establish two topological invariants for characterizing the non-Hermitian phase transitions: (i) with time-reversal symmetry, the biorthogonal ${\mathbb{Z}}_{2}$ invariant based on non-Hermitian Wilson loops, and (ii) without time-reversal symmetry, a biorthogonal spin Chern number through biorthogonal decompositions of the Bloch bundle of the occupied bands. These topological invariants can be applied to a wide class of non-Hermitian topological phases beyond Chern classes, and provides a powerful tool for exploring novel non-Hermitian topological matter and their device applications.

Performance analysis of dwt- ofdm and fft-ofdm systems

Abstract: Performance of Orthogonal Frequency Division Multiplexing (OFDM) systems using Fast Fourier Transforms (FFT) and Discrete Wavelet Transform (DWT) are analyzed in this paper. The performance of DWT-OFDM is assessed by various parameters such as BER, eye diagram and constellation diagram. BER is the ratio of the no. of bits with error to the total no. of bits transmitted through the channel. From the Eye diagram, we can find the eye height through which the interference can be calculated. By varying the different wavelets and the different modulation schemes the BER is calculated and the eye diagram and the constellation diagram are plotted with the aid of MATLAB- SIMULINK. In this work, performance of most widely used wavelet based OFDM systems Haar, Daubechies, Biorthogonal, and Reverse Biorthogonal wavelets are studied and wavelet basis suitable for optimum OFDM system is investigated. Bit Error Rate (BER) versus Signal to Noise Ratio (SNR) is used as system parameter.

Families of biorthogonal wavelets

Abstract: Several families of biorthogonal wavelet bases are constructed with various properties. In particular, for a given filter, Fn(ξ), of finite length 2n + 1, a parametric family of dual filters, FvN(ξ), of length 2N + 1 is constructed. The parametric nature of the dual filters makes it possible to design the optimum dual filter Fv0N(ξ), corresponding to a fixed filter Fn(ξ).

Dynamic correlation for biorthogonal valence bond reference states

Abstract: The use of biorthogonal valence bond reference functions in evaluating the correlation energy is investigated. Since the method is not variationally bound some care must be taken in defining the reference state to ensure that the variational bound is not violated, some discussion is given to this matter. The procedure adopted here is a matrix element driven configuration interaction scheme. To reduce the computational labour involved, a configuration selection criterion is introduced. The method is tested through its application to the symmetric stretching of HF, H2O, (2 B 1) NH2 and the singlet-triplet gap in CH2. Comparison is made with other methods, including full CI. The results show that the current method is quite promising.