Using (1.1), the authors obtained estimations of error for the mid-point, trapezoid, and Simpson quadrature formulae. They also gave applications of the mentioned results in numerical integration and for special means. In this paper, we establish two perturbations of (1.1). Using the perturbations, we derive some new error bounds for the mid-point, trapezoid, and Simpson quadrature formulae. Si...

In this paper, various algorithms for designing quadrature mirror filter are reviewed and a new algorithm is presented for the design of near perfect reconstruction quadrature mirror filter bank. In the proposed algorithm, objective function is formulated using the perfect reconstruction condition or magnitude response condition of prototype filter at frequency (ω = 0.5π) in ideal condition. Th...

Numerical integration is a common sub-problem in many applications. It can be solved easily in CPU-based applications using adaptive quadrature such as the adaptive Simpson’s rule. These algorithms rely, however, on error estimation yielding a significant computational overhead. In addition, they require recursive function evaluations, which are not well suited for parallel computation on graph...

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a ...

Phase error analysis in Temporal Phase Shifting (TPS) algorithms due to frequency detuning has been to date only performed numerically. In this paper, we show an exact analytical expression to obtain this phase error due to detuning using the spectral TPS response. The new proposed method is based on the phasorial representation of the output of the TPS quadrature filter. Doing this, the detuni...

We consider the quadrature method developed by Kravanja and Van Barel (Computing 63(1):69–91, 1999) for computing all the zeros of an analytic function that lie inside the unit circle. The algorithm uses only the function values and no (first or higher order) derivatives. Information about the location of the zeros is obtained from certain integrals along the unit circle. In numerical computati...

In this paper, we propose an Error Concealment algorithm for INTRA-frame losses over packet loss channels. The novelty is that not only the INTRA-frame but also the subsequent INTER-frames are error concealed. We use the received INTRA-MBs to refine their neighbors based on the strong correlation between adjacent pixel values. In addition, Motion Compensation is used to reconstruct the INTER-pi...

Multiplication is the main operation in many signal processing algorithms. High accuracy and low power dissipation are the most important objectives in many multimedia and lossy applications such as filtering, convolution, Euclidean distance, fast Fourier transform (FFT).The fixed width multipliers are used to maintain a fixed format and allow a little accuracy loss of output data. In this pape...

We study the optimal general rate of convergence of the n-point quadrature rules of Gauss and Clenshaw–Curtis when applied to functions of limited regularity: if the Chebyshev coefficients decay at a rate O(n−s−1) for some s > 0, Clenshaw–Curtis and Gauss quadrature inherit exactly this rate. The proof (for Gauss, if 0 < s < 2, there is numerical evidence only) is based on work of Curtis, Johns...

The symbol-error rate (SER) of a quadrature subbranch hybrid selection/maximal-ratio combining scheme for 1-D modulations in Rayleigh fading under employment of the generalized receiver, which is constructed based on the generalized approach to signal processing in noise, is investigated. At the generalized receiver, N diversity branches are split into 2N in-phase and quadrature subbranches. Tr...