Spectral analysis comparisons of Fourier-theory-based methods and minimum variance (Capon) methods

• Fourier theory was used as a reference to study the effect of filter size variation.
• Adaptive filters can be useful but great care is needed in their application.
• Adaptive filters are most useful when a small number of spectra lines are present.
• The filter size sets an upper limit in the number of spectral peaks resolved.
• Radar data deconvolution was used to compare two methods of spectral estimation.

In recent years, adaptive (data dependent) methods have been introduced into many areas where Fourier spectral analysis has traditionally been used. Although the data-dependent methods are often advanced as being superior to Fourier methods, they do require some finesse in choosing the order of the relevant filters. In performing comparisons, we have found some concerns about the mappings, particularly when related to cases involving many spectral lines or even continuous spectral signals. Using numerical simulations, several comparisons between Fourier transform procedures and minimum variance method (MVM) have been performed. For multiple frequency signals, the MVM resolves most of the frequency content only for filters that have more degrees of freedom than the number of distinct spectral lines in the signal. In the case of Gaussian spectral approximation, MVM will always underestimate the width, and can misappropriate the location of spectral line in some circumstances. Large filters can be used to improve results with multiple frequency signals, but are computationally inefficient. Significant biases can occur when using MVM to study spectral information or echo power from the atmosphere. Artifacts and artificial narrowing of turbulent layers is one such impact.