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.

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