Probability Distribution of Spectral Estimates Obtained Via Overlapped FFT Processing of Windowed Data
NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT
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The characteristic function of spectral estimates obtained via overlapped FFT processing of windowed data is presented for a random process containing a signal tone and Gaussian noise. For the special case of noise- alone, the probability distribution of the estimate is plotted and compared with an approximation utilizing only the first two moments and found to be in excellent agreement in probability over the range .0001, .9999 for several data windows, overlaps, and time-bandwidth products. This result means that knowledge of the equivalent degrees of freedom of the spectral estimate is adequate for a complete probabilistic description, even when the overlap results in significant statistical dependence of the component FFT outputs.
- Statistics and Probability
- Non-Radio Communications