We construct an optimal quadrature formula in the sense of Sard in the Hilbert space K2(P3). Using Sobolev’s method we obtain new optimal quadrature formula of such type and give explicit expressions for the corresponding optimal coefficients. Furthermore, we investigate order of the convergence of the optimal formula and prove an asymptotic optimality of such a formula in the Sobolev space L 2...

An integrable current-tunable sinusoidal quadrature oscillator is presented. A current-tunable all-pass filter is used as the frequency-selective network. The implementation is fullybalanced so as to enable accurate quadrature signals with symmetry. The oscillation frequency is currenttunable over a wide-freqency sweep range of approximately three orders of magnitude. The quadrature signals pos...

Single LC oscillators are known for their good phase noise performance. In this paper we analyse the effect of cross-coupling two LC oscillators in order to provide quadrature outputs, which are mandatory in modern transceiver architectures. We present a theoretical study that shows that due to coupling a frequency shift exists and the oscillator quality factor is reduced, leading to a poorer p...

It has been suggested in the literature that different quasi-uniform node sets on a sphere lead to quadrature formulas of highly variable quality. We analyze here the nature of these variations, and describe an easy-to-implement leastsquares remedy for previously problematic cases. Quadrature accuracies are then compared for different node sets ranging from fully random to those based on Gaussi...

A generalized N-point Birkhoff–Young quadrature of interpolatory type, with the Chebyshev weight, for numerical integration of analytic functions is considered. The nodes of such a quadrature are characterized by an orthogonality relation. Some special cases of this quadrature formula are derived. 2011 Elsevier Inc. All rights reserved.

Conditional homodyne detection is proposed as an extension of the intensity correlation technique introduced by Hanbury-Brown and Twiss [Nature (London) 177, 27 (1956)]. It detects giant quadrature amplitude fluctuations for weakly squeezed light, violating a classical bound by orders of magnitude. Fluctuations of both quadrature amplitudes are anomalously large. The squeezed quadrature also ex...

In this paper, we discuss the properties of a quadrature formula with the zeros of the Bessel functions as nodes for integrals ∫ ∞ −∞ |x|f(x)dx, where ν is a real constant greater than −1 and f(x) is a function analytic on the real axis (−∞,+∞). We show from theoretical error analysis that (i) the quadrature formula converges exponentially, (ii) it is as accurate as the trapezoidal formula over...

We report on quadrature demultiplexing of a quadrature phase-shift keying (QPSK) signal into two cross-polarized binary phase-shift keying (BPSK) signals with negligible penalty at bit-error rate (BER) equal to 10(-9). The all-optical quadrature demultiplexing is achieved using a degenerate vector parametric amplifier operating in phase-insensitive mode. We also propose and demonstrate the use ...

A quadrature finite element Galerkin scheme for a Dirichlet boundary value problem for the biharmonic equation is analyzed for a solution existence, uniqueness, and convergence. Conforming finite element space of Bogner-Fox-Schmit rectangles and an integration rule based on the two-point Gaussian quadrature are used to formulate the discrete problem. An H2-norm error estimate is obtained for th...

PURPOSE Carbon-13 magnetic resonance spectroscopy ((13) C-MRS) is challenging because of the inherent low sensitivity of (13) C detection and the need for radiofrequency transmission at the (1) H frequency while receiving the (13) C signal, the latter requiring electrical decoupling of the (13) C and (1) H radiofrequency channels. In this study, we added traps to the (13) C coil to construct a ...