Fourier integrals and quadrature-introduced aliasing

Publisher Website
Google Scholar
Abstract
Computation of Fourier transforms of oscillatory signals by refined quadrature rules using uneven weighting schemes leads to spurious spectral estimates. The degree of spectral contamination can be estimated as a function of frequency by an analysis in terms of aliasing. In particular, the extended Simpson's rule introduces a secondary −13 amplitude aliasing across a folding frequency equal to 12 the Nyquist frequency. This secondary folding frequency is clearly related to the pseudo-sampling interval introduced by the quadrature weighting scheme. Quadrature-introduced aliasing results in spectral contamination within the principal band (0 to fN Hz). An example has been given to demonstrate the quadrature-introduced aliasing and discussed in terms of seismic signals.

This publication has 3 references indexed in Scilit: