Probability Distribution of Spectral Estimates Obtained Via Overlapped FFT Processing of Windowed Data

Abstract

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.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 03, 1976
Accession Number
ADA034753

Entities

People

  • Albert H. Nuttall

Organizations

  • Naval Underwater Systems Center

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Bandwidth
  • Computations
  • Data Science
  • Eigenvalues
  • Equations
  • Fast Fourier Transforms
  • Fourier Transformation
  • Frequency
  • Gaussian Noise
  • Information Science
  • Noise
  • Numbers
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Signal Processing

Readers

  • Approximation Theory.