For spectrum estimation of stationary time series the method of maximum entropy (ME) is compared to the method using fast Fourier transforms (FFT). As the maximum entropy method is highly nonlinear such a comparison is done on the basis of a simulation. The ME method is introduced and it is demonstrated that especially for short data sequences the ME method is capable of delivering superior spectral estimates. How the ME method works and why the ME estimation produces such unexpectedly good results is discussed. Further, the influence of a digitizing signal acquisition apparatus, of additive white noise, and of the initial phase on the variability of the estimated spectra are investigated. Fitting an autoregressive process to the time signal is equivalent to the ME procedure. An autoregressive fit code is presented.

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