Showing papers on "Spectral density estimation published in 1971"

Data Transmission by Frequency-Division Multiplexing Using the Discrete Fourier Transform

Abstract: The Fourier transform data communication system is a realization of frequency-division multiplexing (FDM) in which discrete Fourier transforms are computed as part of the modulation and demodulation processes. In addition to eliminating the bunks of subcarrier oscillators and coherent demodulators usually required in FDM systems, a completely digital implementation can be built around a special-purpose computer performing the fast Fourier transform. In this paper, the system is described and the effects of linear channel distortion are investigated. Signal design criteria and equalization algorithms are derived and explained. A differential phase modulation scheme is presented that obviates any equalization.

On Detecting a Signal in N Stationarily Correlated Noise Series

Abstract: A useful model in the analysis of multiple time series is to assume that each series is composed of a fixed signal common to all series and a wide sense stationary normal noise process. If the noise series are uncorrelated with identical autocorrelation functions, we have in the time domain a collection of independent normal vectors with a common covariance matrix. The likelihood ratio statistic for detecting the signal is then a singular version of Hotelling's T 2. In this paper, a likelihood ratio test utilizing the asymptotic properties of the finite Fourier transform leads to an asymptotically non-singular frequency domain version of Hotelling's T 2. It is shown that the F statistic for detecting the signal depends only upon certain spectral power measurements with the Type I error and signal detection probabilities determined from existing tables for the central and non-central F distributions. Several examples are presented illustrating the detection procedure.

A Fast Fourier Transform for High-Speed Signal Processing

Abstract: An arbitrary-radix fast Fourier transform algorithm and a design of its implementing signal processing machine are introduced. The algorithm yields an implementation with a level of parallelism proportional to the radix r of factorization of the discrete Fourier transform, allows 100 percent utilization of the arithmetic unit, and yields properly ordered Fourier coefficients without the need for pre- or postordering of data.

Spectral Estimation by Means of Overlapped Fast Fourier Transform Processing of Windowed Data

Abstract: : An investigation of power-density autospectrum estimation by means of overlapped Fast Fourier Transform (FFT) processing of windowed data is conducted for four candidate spectral windows with good side-lobe behavior A comparison of the four spectral windows is made on the basis of equal half-power resolution bandwidths The criteria for comparison are statistical stability of the spectral estimates, leakage (side lobes) of the spectral windows, number of FFTs (number of overlapped pieces) required, and size of each FFT required Some striking invariances are discovered in the ultimate variance-reduction capabilities and in the number of FFTs required to realize 99 percent (or less) of the maximum EDF The only trade-off among the four windows is that those with better side lobes require larger-size FFTs

Optical information processing using variable electro-optic spatial filter

Abstract: Apparatus is disclosed including an optical information processing system including a variable electro-optic spatial filter including an electro-optic medium having a characteristic that varies as a function of the intensity of an associated electric field, means for applying an electric field to the electro-optic medium, means for providing to the electro-optic medium a first Fourier transform of radiation representative of information to be processed, means for varying the intensity of the associated electric field to vary the characteristic of the electro-optic medium in a predetermined pattern for modulating information of predetermined spatial frequency included in the first Fourier transform, to produce a modified form of the first Fourier transform, and means for providing a second Fourier transform of the modified form of the first Fourier transform to reproduce a replica of the radiation representative of information to be processed with information of predetermined spatial frequency modified in accordance with the intensity pattern of the associated electric field.

Spectral Estimation from Irregularly Spaced Data

Abstract: Observational data often is irregularly taken or has large gaps due to instrument failure or other real world effects. Yet no spectral estimation theory in use allows one, without dubious interpolation, to estimate spectra from an irregularly sampled signal, nor to combine pieces of record to estimate power at periods longer than the longest piece. A natural extension of conventional complex demodulation is proposed and illustrated for estimating auto- and cross-spectra. The sampling times can be randomly spaced and need not even be in order. The method reduces to the usual method when the data are equally spaced.

On‐Line Digital Spectral Analysis

Abstract: The paper describes a straightforward spectral analysis system using the fast Fourier transform algorithm and an on‐line digital computer in the laboratory. The technique is backed by a sound mathematical foundation and yields directly both components of the cross spectrum for a process measured at two points as well as the power spectrum at either point. For a potential user, certain of the details of implementing the system are included. A specific example, that of correlating density fluctuations in a plasma, demonstrates the sensitivity of such a system.

Alias-Free Spectral Estimation of Stochastic Processes

Abstract: A scheme for the practical estimation of power spectrum from randomly-timed samples is proposed and investigated for wide-sense stationary point processes. The sampling process {tn} is assumed to be stationary point process statistically independent of the sampled process X(t). Stationarity of {tn} admits that joint statistics of tk, tk+n do not depend on k. Closed form analytical formulae are derived for the spectral window Qm(f) and for cov{S^(fr), S^(fq)}, var{S^(fr)} for the particular case of independent identically distributed sampling intervals. Results confirm the alias-free character of the Poisson sampling scheme even for non-bandlimited spectra. It is shown further that for Gaussian processes with very smooth spectra Poisson sampling process can yield more reliable estimates (i.e., with a smaller variance) than the well known method of periodic sampling.

An Electrical and Statistical Study of Burst Noise

Abstract: Burst noise is a normally undesirable phenomenon occasionally found in bipolar semiconductors and other current carrying devices. It is an electrical fluctuation which exhibits itself as one or more rectangular waveforms possessing constant amplitude but random pulse duration. The experimental portion of this study relates only to burst noise in bipolar transistors and operational amplifiers. Burst noise is not Gaussian as are the more common fluctuations in semiconductors. That fact was established by estimation of the amplitude distribution, a technique found to be sensitive in the detection of burst noise obscured by quantities of conventional noise. The amplitude of burst noise varies with the parameters of base-emitter, voltage temperature and source resistance. An exponential increase of amplitude with Vbe and a lack of dependence on collector voltage implied that the noise originates in the base-emitter junction. A noise magnitude linearly proportional to source resistance over several decades leads one to infer the equivalent circuit of a current source between base and emitter. Current amplitudes of 10-10 to nearly 10-6 ampere p-p were observed. Burst noise pulse durations were found as brief as 10 µsec and as long as some 29 hours; neither an upper nor a lower bound was established. The two noise states (high and low, in the rectangular waveform) were treated separately in the duration experiments. Careful measurements on the relative frequency with which the pulse occurred gave duration probability densities of 1/τ e -t/τ for each state. That density also applies to a single particle alternately being trapped and escaping and is consistent with the physical theory due to Mead and Whittier relating burst noise to trapping phenomena. Measurements on noise pulse durations in both states as a function of Vbe lent support to the theory and indicated both trapping and recombination-generation centers were present in samples examined. Another theory, due to Leonard and Jaskolsky, was found inconsistent with the evidence for burst noise's origin in the base-emitter junction. Duration versus temperature dependence indicated activation energies of roughly .5 eV. Although suggestions in the literature for the power spectrum of burst noise have been inconsistent, digital spectral estimation and judicious use of a wave analyzer showed the spectrum to be flat at low frequencies and to fall as 1/f2 at higher ones. Proceeding only from the measured pulse duration probability density, the power spectrum was deduced on theoretical grounds for the first time. The method entailed the derivation of burst noise's autocorrelation function which, when Fourier transformed, yielded S(w) = 2/(τ1 + τ0)[(1/τ1 + 1/τ0)2 + w2] where τ1 and τ0 are the average durations in the two noise estates. The expression proved consistent with experiment.

Analysis of the acoustic signature of dungeness crabs (Cancer magister)

Abstract: Acoustic signals from Dungeness crabs of known size and sex have been collected and analyzed The digital analysis included computation of the autocorrelation function and the power spectral density of each signal The relationship between spectral resolution, statistical error and signal length was considered Several different spectral windows were applied The width of the window was found to have a greater effect on the spectrum than did the type of window Results of the analysis to date indicate that it may be possible to identify the sex of a crab from its acoustic signature Effective and practical methods of recovering and analyzing the acoustic signatures of marine species could lead to a remote detection and identification technique Success with such a technique should contribute to both more efficient harvesting and more effective management of marine resources

A time-varying power spectrum

Abstract: A lime-varying power spectrum is developed for the BIFORE or Hadamard transform (BT or HT) [1], [2]. This spectrum can be used for the purposes of on-line power spectral analysis in several areas where BT has already found applications [3]-[7].