POTENTIAL FREQUENCY-RESOLUTION CAPABILITIES OF SPECTRAL ANALYSIS

Abstract

Many new practical methods of geophysical harmonic analysis appeared in the 1970's, including the Burg maximum-entropy method, the Pisarenko harmonic expansion method, the Capon spectral maximum-likelihood method, and their parametric and non-parametric extensions. The objective of all of these methods was to improve frequency resolution in short times series, and they therefore become known as improved frequency resolution methods. There then arose a need for quantitative evaluation of the resolution attainable by these methods and for comparison of their relative effectiveness. In this connection, the author earlier investigated the harmonic expansion method. (HEM) and demonstrated that its resolution is given by the expression T1/6Δω > 1, where Δω is the spacing of the peak frequencies and T is the observation time in the series. The present paper discusses the maximum resolution of harmonic analysis. The author demonstrates that it is given by T5/4Δω > 1 for common-origin signals and by T7/6 Δω > 1 when the peak harmonics have different initial phases. Although the latter is a special case, its applied significance is as great as the other.