Showing papers on "Spectral density estimation published in 1968"

Signal energy distribution in time and frequency

Abstract: The Fourier representation of signals and its relation to the signal structure in time and frequency, and more generally the inherent properties of phase-modulated signals, have received considerable attention in the past. These topics have led to such seemingly unrelated studies as the representation of a signal in a combined time-frequency plane, "instantaneous power spectra," and the ambiguity function and its transform relations. It is shown in this paper that the studies can be unified by the introduction of the concept of the complex energy density function of a signal. The function is an extension and combination of the one-dimensional energy density functions in time and frequency, the energy density spectrum |\Psi(f)|^{2} , and energy density waveform |\psi (t)|^{2} . On the basis of the complex energy density function, the significance of complicated-appearing transform relations is readily understood. The new concept also conveys a good insight into the internal structure of phase-modulated signals.

The application of the discrete Fourier transform in the estimation of power spectra, coherence, and bispectra of geophysical data

Abstract: The computation of power spectra, cross spectra, coherence, and bispectra of various types of geophysical random processes is part of the established routine. Since it is routine, some of the standard procedures need to be examined rather carefully to be certain that the assumptions behind the procedures are applicable to the data on hand. The basic criteria for a particular method are its resolution bandwidth, its variance, and its bias. In this paper several basic power-spectrum estimation procedures are reviewed and their statistical and mathematical properties are discussed. The direct use of the discrete Fourier transform for various spectrum calculations is discussed in detail, and its properties are compared with the standard procedure that uses the cosine transform of the estimated correlation function.

Statistical spectral analysis (single channel case) in 1968.

Abstract: : Statistical spectral analysis is a technique for data analysis which computes from observed functions of time various functions of a variable called frequency. The record can consist of a single function X(.) of time (single channel case) or of several functions of time X sub 1(.),...,X sub n(.) (multi-channel case). This paper describes the view that to understand statistical spectral analysis in 1968 one must comprehend three distinct aspects: (1) how to define the spectrum, (2) how to compute the spectrum (four methods are distinguished: filtering, smoothed periodogram, covariance averages or filtered periodogram, autoregressive), and (3) how to interpret the spectrum (especially with regard to testing for hidden periodicities, estimation of the spectral density, and mixed spectral estimation). The effect of Fast Fourier Transform techniques on statistical spectral analysis is also discussed. A basic theorem on the means, variances, and covariances of filtered sample spectral density functions is stated. (Author)

A Digital Processor to Generate Spectra in Real Time

Abstract: —A digital processor capable of computing the discrete Fourier transform for a range of audio signals in real time has been built as part of a facility to conduct research in signal processing. The digitized sample values can be complex. The arithmetic unit is configured to perform complex connectives, and automatic array scaling is used to make numerical accuracy independent of signal level. The Cooley–Tukey "fast Fourier transform" is the algorithm used.

Communication at Low Date Rates--Spectral Analysis Receivers

Abstract: The purpose of this paper is to introduce a multiple frequency shift keying spectral analysis receiver based on the fast Fourier transform. A novel decision-directed automatic frequency control (AFC) for use with the fast Fourier receiver is mentioned. Not only is the system to be described better than a truncated autocorrelation receiver, the analysis required is unorthodox, being based on the fact that the spectral coefficients of the incoming waveform are chi-square (central or noncentral) distributed. The fast Fourier receiver, under typical conditions, is 1.5 dB better than the autocorrelation receiver, is more versatile (e.g., tone spacing to multiples of 1/T Hz, spectral window shaping very easy), easier to implement, less subject to signal-to-noise ratio degradation due to frequency offset, and provides fine frequency information to operate a decision-directed AFC.