Statistical Characteristics of Power Spectrum Estimates Derived from Higher Resolution FFT'

摘要

This report documents an investigation of the properties of a technique used to reduce the resolution of a power spectrum estimate. The technique investigated is the familiar one in which averaging across frequency is performed on a spectrum estimate to produce an estimate which has less resolution, but improved stability. Results are presented in various areas. Primarily, the statistical nature of a reduced resolution spectrum produced in this way is characterized by the derivation of expressions for equivalent degrees of freedom. In addition, the associated spectral windows are determined, and examples are shown which illustrate the effect on the spectrum estimate of various uniform and non-uniform weighting schemes in the frequency averaging. Finally, a particular weighting scheme is shown which produces results which closely approximate the lower resolution estimate obtained by conventional means with the Hanning window. (Author)