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Fourier integrals and quadrature-introduced aliasing

SEISMOGRAPHIC STATION DEPARTMENT OF GEOLOGY AND GEOPHYSICS UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA

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 amplitude aliasing across a folding frequency equal to 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 f_N Hz). An example has been given to demonstrate the quadrature-introduced aliasing and discussed in terms of seismic signals.

Footnotes

^* On educational leave from: Department of Geophysics and Geodesy, University of Chile, Santiago, Chile.