Showing papers on "Spectral density estimation published in 1969"

Fourier transform recording with random phase shifting

Abstract: In making a record of the exact Fourier transform of an array of beams of electromagnetic radiation, the phase of each of a substantial fraction of the beams is shifted by a constant amount before recording the transform.

Design Considerations in Power Spectra Measurements by Diffraction of Coherent Light

Abstract: The estimation of the spectral density of a spatial random process by diffraction requires that the parameters of the diffraction system be compatible with the statistical properties of the process. Otherwise, the estimate of the spectrum can be unstable or unduly biased. The relation between the second-order statistics of the process and the parameters of a basic diffraction system that are required for reasonable spectral estimates is investigated. Such parameters include aperture dimensions, wavelength, focal length of the lens, and scanning slit size. With the typical diffraction system, it is difficult to estimate the power spectrum because of the presence of the zero-order aperture-diffracted light. A technique is furnished in this paper for spectral estimation at dc. Experimental results are furnished for film grain and total film noise. It is shown that the residual phase noise of film at dc even under so-called matched conditions is large enough to prevent the accurate estimation of the dc value of grain noise.

Clipping Loss in the One‐Bit Autocorrelation Spectral Line Receiver

Abstract: An error analysis of the one-bit autocorrelation method of spectral estimation is presented, and the variance on the autocorrelation estimate and spectral estimate is given. In the nonclipped (many-bit) case, the normal Nyquist sampling rate of 2B is sufficient. Higher sampling rates do not further improve the spectral estimate. In the clipped (one-bit) case, increasing the sampling rate does improve the estimate. The present work was initiated to examine this effect. The results verify the decrease in spectral variance with increased sampling rate. Itis shown that a part of the signal-to-noise deterioration caused by the clipping may be removed by the higher sampling. An increased sampling rate from 2B to 4B, however, achieves most of the available improvement.

Factorization of spectra by discrete Fourier transforms

Abstract: Discrete Fourier transform method for factoring spectral density functions, calculating absolute error

Phase Free Estimation of Coherence

Abstract: A phase free estimate of the coherence of a bivariate Gaussian process is presented. The technique is based on the usual independent, complex normal approximation to the distribution of the finite Fourier transform of a multivariate stationary time series, and the complex Wishart approximation to the distribution of spectrum estimates. If the spectral densities and coherence can be assumed to be constant over a wider frequency band than the phase can be assumed to be constant, the concept of inner and outer spectral windows would seem appropriate. Maximum likelihood estimates of the coherence are obtained using phase free marginal distributions at the inner window level. The results of simulations are presented showing the likelihood for various inner windows.

Effects of quantization and sampling in digital correlators and in power spectral estimation

Abstract: An efficient method for calculating the mean values and standard deviations of spectral estimates and decision variables is described which utilizes Kellogg's numerical method for calculating correlation functions of quantized random waveforms. The method and computer program are designed to explore the interaction between sampling (i.e., aliasing) and quantization effects.

Application of Gabors Elementary-Signal Theorem to Estimation of Nonstationary Human Spectral Response

Abstract: This paper addresses the problem of forming sequential gain and phase estimates needed to permit direct study of time variations in human response. The conventional Fourier transform with "boxcar" data window is shown to be unsatisfactory. Gabor's theory of elementary signals is cited to show that Fourier transformation with Gaussian data weighting yields an optimum combination of spectral and time resolution. For this window the estimation procedure is constrained by the fundamental relationship ?? . ?t = ? where ??, ?t are the standard deviations of weights across the spectral and data windows, respectively. The Gabor (Gaussianweighted Fourier) transform is introduced. Some consequences of implementing this procedure are briefly discussed and empirical results are presented in verification.

Estimation of direct and cross power spectral density of discrete data using the fast Fourier transform

Abstract: Direct and cross power spectral density estimation of discrete data using fast Fourier transform with digital filter solution

A hybrid method for cross-power spectral density estimation

Abstract: A hybrid scheme for estimation of cross-power spectral density is presented, where filtering is analog and averaging is digital. Expressions of the expected value, and of the dispersion of the estimate so achieved, are obtained. Indications for estimate design are then given.