Algorithms for Optimal Numerical Quadrature Based on Signal Class Models
de Figueiredo, Rui J.P.
Numerical quadrature; numerical integration; moments; convolution; Fourier transforms; filters; spline functions; variational methods
A framework is presented for constructing various types of numerical quadrature algorithms which take into account the a-priori known or estimated properties of the signal being processed. This is done by appropriately modeling the signal class to which such a signal belongs. Both linear and nonlinear signal class models are considered and wide use of generalized spine theory is made. For the nonlinear case, a new type of nonlinear generalized spline is defined.