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 fN Hz). An example has been given to demonstrate the quadrature-introduced aliasing and discussed in terms of seismic signals.