The Effect of Interpolation of Data Upon the Harmonic Coefficients

摘要

The practice of interpolating irregularly spaced data to obtain 'representative' values at equally spaced points along the abscissa is quite common in harmonic analysis applications. This interpolation may 'distort' the data sufficiently to cause the spectrum of the interpolated data to bear little resemblance to the original spectrum, especially at high frequencies. The effect of linear interpolation of the data upon its harmonic coefficients is discussed in this report. High frequency waves in the data tend to be destroyed by interpolation and their variance redistributed to other frequencies. When the original data do not contain a particular harmonic, the expected value of the amplitude of that harmonic in the interpolated data varies as a multiple of a Rayleigh variable. The multiplier is a function of the frequencies and amplitudes of the harmonics in the original data and the frequency of the particular harmonic under investigation. Complete folding does not occur. Partial folding or no folding at all can be expected. Tables containing the expected values of some harmonic amplitudes of the interpolated data for various types of original data are provided for comparison purposes. (Author)