Showing papers on "Spectral density estimation published in 1970"

A Pipeline Fast Fourier Transform

Abstract: This paper describes a novel structure for a hardwired fast Fourier transform (FFT) signal processor that promises to permit digital spectrum analysis to achieve throughput rates consistent with extremely wide-band radars. The technique is based on the use of serial storage for data and intermediate results and multiple arithmetic units each of which carries out a sparse Fourier transform. Details of the system are described for data sample sizes that are binary multiples, but the technique is applicable to any composite number.

On Multivariate Density Estimates Based on Orthogonal Expansions

Abstract: The topics of orthogonality and Fourier series occupy a central position in analysis. Nevertheless, there is surprisingly little statistical literature, with the exception of that of time series and regression, which involves Fourier analysis. In the last decade however, several papers have appeared which deal with the estimation of orthogonal expansions of distribution densities and cumulatives. Cencov [1] and Van Ryzin [6] considered general properties of orthogonal expansion based density estimators and the latter applied these properties to obtain classification procedures. Schwartz [3] and the authors [2] and [4] investigated respectively the Hermite and Trigonometric special cases. The authors also obtained certain general results which apply not only to estimators of the population density but also to estimators of the population cumulative [2], [4] and [5]. In this paper several results derived for the univariate case are extended to the multivariate case. Also a new relationship is obtained which involves general Fourier expansions and estimators. Although there is some reason for calling the Gram-Charlier estimation of distribution densities a Fourier method, one fundamental aspect of Fourier methods is not shared by Gram-Charlier estimation. Gram-Charlier techniques make no use of Parseval's Formula or related error relationships of Fourier analysis. The ease with which the mean integrated square error (MISE) is evaluated, when Fourier methods are applied, accounts for most of the recent interest in this area. Section 1 of this paper deals with an investigation of two general MISE relationships for multivariate estimates of Fourier expansions. The relationship given in Theorem 2 is particularly simple and yet includes the four MISE's which are involved in the estimation problem. In Section 2 the choice of orthogonal functions is restricted to the trigonometric polynomials. It is shown that the MISE of multidimensional trigonometric polynomial estimators are related in a simple way to the Fourier coefficients of the distribution which is being estimated. This result is of considerable utility since it yields a rule for deciding which terms should be included in the estimate of the multivariate density.

An improved algorithm for high speed autocorrelation with applications to spectral estimation

Abstract: A common application of the method of high speed convolution and correlation is the computation of autocorrelation functions, most commonly used in the estimation of power spectra. In this case the number of lags for which the autocorrelation function must be computed is small compared to the length of the data sequence available. The classic paper by Stockham, revealing the method of high speed convolution and correlation, also discloses a number of improvements in the method for the case where only a small number of lag values are desired, and for the case where a data sequence is extremely long. In this paper, the special case of autocorrelation is further examined. An important simplification is noted, based on the linearity of the discrete Fourier transform, and the circular shifting properties of discrete Fourier transforms. The techniques disclosed here should be especially important in real-time estimation of power spectra, in instances where the data sequence is essentially unterminated.

Spectral estimation for transient waveforms

Abstract: For steady-state waveform analysis, the classical (possibly smoothed) periodogram of the sampled waveform gives one an adequate spectral representation. For transient waveforms of unknown duration in noise, however, the periodogram generally fails in that it is tied to a fixed time interval. As an alternative, a digital computer program which will do time-varying spectral estimation has been developed. Briefly, the program may be described as a digital equivalent of a constant Q-comb filter bank wherein one can vary the frequency range covered and the frequency resolution (i.e., the Q). For a given specified frequency range, as one increases the frequency resolution, the program automatically selects more filters and spaces them so as to cover the specified frequency range; the various contiguous filters are overlapped at the -3 dB points. The instantaneous energy contained in each filter is used to modulate the z axis of a CRT display and hence provide a time-frequency-intensity plot of the time-varying spectrum. Results obtained from the computer program upon real data are given.

Factorization of spectra by discrete Fourier transforms (Corresp.)

Abstract: A discrete Fourier transform method for factoring arbitrary spectral density functions is presented. The factorization can be implemented in a straightforward and efficient manner, and it does not require that the spectra be rational. An expression for the absolute error is also presented.

A special-purpose online processor for bandpass analysis

Abstract: The design of a special-purpose on-line processor for bandpass analysis with application to spectral estimation is described. The processor utilizes a digital filtering procedure based on the frequency shift of the sampled signal spectrum. A peculiarity of the processor is that it performs a bandpass analysis by using a unique set of digital filter coefficients for all the analyzed bands. A small and simple memory is therefore used as coefficient memory, while a special, but not complex, organization with many sections is required for the sample memory. The processing of an audio signal to obtain a type of digital vocoder is also considered. From the point of view of the actual implementation, only MSI and LSI circuits are used for the memory and arithmetic units.

A spectral analysis program for the processing of neuro-electric data

Abstract: The Spectral Analysis Program is designed to perform the following kinds of spectral analysis, using the Cooley-Tukey Fast Fourier Transform Algorithm: cross correlation, cross power spectrum, Fourier transform, inverse Fourier transform, and double Fourier transform (the process of transforming two real functions simultaneously). These operations are performed on two blocks of core that can be filled through time-sequential sampling of an external analog signal or from previously sampled data that have been stored on DECtape. Through the use of nine Teletype commands, the user can manipulate input and output and select a particular type of spectral analysis. Output may be displayed on a 30D scope stored on DECtape or turned into hard copy by a Calcomp plotter used for processing neuroelectric data at the Stanley Cobb Laboratories for Psychiatric Research.