Mathematical analysis of spectral estimation algorithms resolution

Abstract

The classical methods of evaluating the energy spectra of discretized deterministic and stochastic processes are generally based on the use of procedures that use the fast Fourier transformation (FFT). The classical approach to spectral analysis is effective in respect of computational and provides asymptotically reliable estimates for very extensive classing signals, satisfying the hypothesis of stationary, ergodicity and limits the large sample volume. Limitations of classical spectral estimates especially apparent when analyzing short data records. However, just such a situation is typical for most practical applications, because many processes have measurable short duration or rapidly changing spectra in time.