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Showing papers on "Spectral density estimation published in 1977"


Journal ArticleDOI
Jont B. Allen1
TL;DR: In this article, a theory of short term spectral analysis, synthesis, and modification is presented with an attempt at pointing out certain practical and theoretical questions, which are useful in designing filter banks when the filter bank outputs are to be used for synthesis after multiplicative modifications are made to the spectrum.
Abstract: A theory of short term spectral analysis, synthesis, and modification is presented with an attempt at pointing out certain practical and theoretical questions. The methods discussed here are useful in designing filter banks when the filter bank outputs are to be used for synthesis after multiplicative modifications are made to the spectrum.

899 citations


Journal ArticleDOI
TL;DR: In this article, the Burg reflection-coefficient method for maximum entropy (antoregressive) spectral estimation is generalized to apply to multichannel complex signal, and it is shown that all resulting power matrices are positive definite.
Abstract: The Burg reflection-coefficient method for maximum entropy (antoregressive) spectral estimation is generalized to apply to multichannel complex signal. It is shown that all resulting power matrices are positive definite. Preliminary numerical results obtained for a monochromatic signal with noise indicate that the determinants of the power matrices are rapidly reduced as the number of filter coefficients is increased, and that superior spectral resolution can be expected.

142 citations


Journal ArticleDOI
TL;DR: The results of spectral estimation of EEGs using the multivariate AR, AR-MA, and conventional windowed periodogram analysis are compared and a new two-stage least-squares procedure is shown.

75 citations


Journal ArticleDOI
TL;DR: The estimate obtained is shown to be strongly consistent and asymptotically normally distributed and the relation between the estimate and that obtained from a high order autoregression is discussed.
Abstract: Spectral methods are used to construct an estimate of the variance of the prediction error for a normal, stationary process. The estimate obtained is shown to be strongly consistent and asymptotically normally distributed. Some aspects of the computations with respect to the fast Fourier transform are considered. The latter half of the article consists of a number of simulations, based on both generated and real data, which illustrate the results obtained. The relation between the estimate and that obtained from a high order autoregression is discussed.

60 citations


Patent
Choquet Michel1
21 Jun 1977
TL;DR: In this paper, a method for determining the initial values of the coefficients of a transversal equalizer in a data transmission system in which the transmission channel creates frequency shift is presented.
Abstract: A method of and apparatus for determining during an initial training period the initial values of the coefficients of a transversal equalizer in a data transmission system in which the transmission channel creates frequency shift. The received periodic training sequence is modulated by a time-domain window signal whose Fourier transform exhibits a relatively flat central peak and has comparatively low values in the vicinity of those frequencies which are a multiple of the inverse of the period of the transmitted sequence, and the discrete Fourier transform Wk of the modulated signal is computed. The values of the coefficients of the equalizer are obtained by computing the inverse discrete Fourier transform of the ratio Fk =Zk /Wk, where Zk is the discrete Fourier transform of the transmitted sequence.

58 citations


Book ChapterDOI
01 Jan 1977
TL;DR: This paper reviews the Fourier methods and compares them to the new techniques in terms of signal models assumed by the three basic methods and their ability to distinguish multiple sinusoids in noise.
Abstract: Spectral estimation often forms the basis for distinguishing and tracking signals of interest in the presence of noise and for extracting information from the received data. The application of Fourier techniques to the problem of estimating the properties of sinusoids in noise dates back as far as Shuster (1898), Fourier spectrum analysis is the basis for almost all spectral-estimation equipment, * including the common sweeping-filter spectrum analyzer, the parallel filter bank, the fast Fourier transform (FFT), the delay-line time compressor (Deltic), and the compressive spectrum analyzer (Microscan). A problem with Fourier spectrum analysis, however, is that it makes implicit assumptions concerning data outside the observation interval and, frequently, these physically unrealistic assumptions reduce the quality of the estimates. During the past decade, two radically different non-Fourier spectral-estimation techniques have emerged — maximum-entropy spectrum analysis (Burg, 1967) and spectral decomposition (Pisarenko, 1973). These techniques offer alternative and often more realistic data models which, in many cases, lead to better estimation performance. This paper reviews the Fourier methods and compares them to the new techniques in terms of signal models assumed by the three basic methods and their ability to distinguish multiple sinusoids in noise.

50 citations


Proceedings ArticleDOI
01 May 1977
TL;DR: In this paper, the authors simplify the concepts of the zoom transform and remove some of the restrictions assumed by Yip; i.e., the total number of points need not be a power of 2.
Abstract: A recent paper by Yip discussed the zoom transform as derived from the defining equation of the FFT. This paper simplifies the concepts and removes some of the restrictions assumed by Yip; ie., the total number of points need not be a power of 2. The technique is based on first specifying the desired center frequency, bandwidth, and frequency resolution. The signal is then sampled, modulated, and lowpass filtered. This result is purposely aliased, then transformed using an FFT algorithm. The result is an M-point frequency spectra of the desired bandwidth centered about the center frequency with a higher degree of resolution than could be directly obtained using an M-point transform.

49 citations


Proceedings ArticleDOI
T. Parks1, J. Wise1
01 Dec 1977
TL;DR: In this paper, the pitch period of voiced speech was determined by a maximum likelihood estimation problem for an unknown periodic signal in white Gaussian noise of unknown intensity, where the problem is to find a filter which passes a periodic signal of period P without distortion while simultaneously suppressing a noise signal having a known spectrum.
Abstract: The problem of determining the pitch period of voiced speech is formulated as a maximum likelihood (ML) estimation problem for an unknown periodic signal in white Gaussian noise of unknown intensity. Modifications of the ML estimator for speech include removal of bias, derivation of a measure of confidence, and prefiltering for non-white noise. The pitch estimation procedure is evaluated in the frequency domain and related to comb filtering. An alternate derivation of the ML estimator, related to the procedure proposed by Lacoss for maximum likelihood spectral estimation is presented. The problem formulated is to find a filter which passes a periodic signal of period P without distortion while simultaneously suppressing, in an optimum manner, a noise signal having a known spectrum.

47 citations


Journal ArticleDOI
TL;DR: Simulation results indicate that line tracking using autoregressive spectral estimates can be accomplished for rapidly time-varying spectra with low signal-to-noise ratios (SNR) or closely spaced spectral lines.
Abstract: This paper presents two new algorithms for tracking spectral lines of signals with time-varying spectra using a sequence of autoregressive spectral estimates. The algorithms are designed to discard false peaks due to noise and signal interference, and with the aid of high resolution autoregressive spectral estimates have the ability to track multiple lines. Simulation results indicate that line tracking using autoregressive spectral estimates can be accomplished for rapidly time-varying spectra with low signal-to-noise ratios (SNR) or closely spaced spectral lines.

25 citations



Journal ArticleDOI
TL;DR: It is shown that a density of bounded variation on S1 can be approximated as closely as desired by such a representation in the space of square-integrable functions on S^{1} .
Abstract: A new representation, called an exponential Fourier density, of a probability density on a circle, S^{1} is introduced. It is shown that a density of bounded variation on S^{1} can be approximated as closely as desired by such a representation in the space of square-integrable functions on S^{1} . The exponential Fourier densities have the desirable feature of being closed under the operation of taking conditional distributions. Facilitated by the use of these densities, finite-dimensional, recursive, and optimal estimation and detection schemes are derived for some simple models including a PSK communication system. A deficiency of the exponential Fourier densities is that they are not closed under convolution. How to circumvent this deficiency is still an open question.

Journal ArticleDOI
TL;DR: In this article, the authors used autoregressive (AR) data modelling, originally introduced by Burg as maximum-entropy spectral analysis, for the analysis of natural seismic events produced by a small earthquake.
Abstract: This paper presents results illustrating the use of high-resolution spectral estimation methods in the analysis of natural seismic events produced by a small earthquake. The methods used are based on autoregressive (AR) data modelling, originally introduced by Burg as maximum-entropy spectral analysis. In addition, a recently proposed adaptive AR method is also examined. Comparisons with conventionally generated power spectra show that the higher resolution spectra computed using the AR technique provide additional useful information for these data. The adaptive AR results indicate that the signatures may be characterized by the early arrival of a high-frequency component near 0.009 Hz which decays to a value of 0.007 Hz at 25 s after onset.

Book ChapterDOI
01 Jan 1977
TL;DR: In this paper, a technique based on an orthogonal decomposition of the cross (discrete) frequency correlation matrix describing the set in the presence of additive uncorrelated noise is proposed.
Abstract: A technique is proposed for the extraction of spectral signals for which the components within a signal set are characterized by complex envelopes which exhibit correlation The technique is based on an orthogonal decomposition of the cross (discrete) frequency correlation matrix describing the set in the presence of additive uncorrelated noise Certain advantages of the technique relative to those based on Fourier analysis with either estimated power spectrum or minimum variance processing are presented Specifically, it is illustrated how the detection performance of the technique is established by the total energy in the spectral set rather than by the levels of individual spectral elements in the set Furthermore, it is shown how minimum variance spectrum analysis actually can suppress components in such a set

Journal ArticleDOI
TL;DR: Observed patterns from the Beatquency Domain suggest usefulness of this method in sleep cycle detection and a new and unusual application of the FFT on heart rate data.
Abstract: Fourier analysis has proven to be a vital mathematical tool in many areas of research, but rapid methods for calculating frequency content of sampled data using discrete Fourier transform (FFT) require periodic sampling. Unfortunately, beat-by-beat heart rate is an aperiodic series of events in the time domain. This report describes a new and unusual application of the FFT on heart rate data. The beat-by-beat intervals are represented as the magnitude of a periodically sampled function. When the Fourier transform is applied to these data, we obtain pseudofrequency information from what we call the Beat-quency Domain. Observed patterns from the Beatquency Domain suggest usefulness of this method in sleep cycle detection.

Journal ArticleDOI
TL;DR: An interpolation technique (interpolation by repetitive convolution) is proposed which yields values accurate enough for plotting purposes and which lie within the limits of calibration accuracies and is shown to operate faster than zero fill, since fewer operations are required.
Abstract: Zero fill, or augmentation by zeros, is a method used in conjunction with fast Fourier transforms to obtain spectral spacing at intervals closer than obtainable from the original input data set. In the present paper, an interpolation technique (interpolation by repetitive convolution) is proposed which yields values accurate enough for plotting purposes and which lie within the limits of calibration accuracies. The technique is shown to operate faster than zero fill, since fewer operations are required. The major advantages of interpolation by repetitive convolution are that efficient use of memory is possible (thus avoiding the difficulties encountered in decimation in time FFTs) and that is is easy to implement.

Proceedings ArticleDOI
Harvey F. Silverman1
01 May 1977
TL;DR: One "General-N" (i.e. many allowable DFT sizes (N) but certainly not any vector size) complex WFTA programming technique is described.
Abstract: The Winograd Fourier Transform Algorithm (WFTA) requires about 20% of the multiplications used in an optimized FFT, while the number of additions remains unchanged. This paper describes one "General-N" (i.e. many allowable DFT sizes (N) but certainly not any vector size) complex WFTA programming technique.

24 May 1977
TL;DR: In this paper, the maximum entropy spectral analysis (MESA) was proposed for radar data processing, which can be used for range-Doppler sizing and coherent measurement of range rate.
Abstract: : For most applications in radar data processing, the Fourier transform performs satisfactorily. However, other methods of spectral analysis can offer some advantages when a data set is too short for a Fourier transform to resolve or detect important spectral features. This report describes one alternative technique, maximum entropy spectral analysis (MESA), and suggests possible radar applications including range-Doppler sizing and the coherent measurement of range rate. Practical examples demonstrate an improvement in velocity resolution and cross-range resolution. Computer codes are listed that calculate MESA power spectra for a real or complex discrete time series. (Author)

Book ChapterDOI
01 Jan 1977
TL;DR: The statistical correlations described in the preceding chapter are useful in turbulence analyses and are relatively easy to measure as discussed by the authors, however, another powerful tool for describing turbulence is the method of spectral analysis, which can describe the exchange of kinetic energy associated with different eddy sizes or with different fluctuation frequencies occurring in the turbulence.
Abstract: The statistical correlations described in the preceding chapter are useful in turbulence analyses and are relatively easy to measure. However, another powerful tool for describing turbulence is the method of spectral analysis. The spectral theory and the correlation theory are intimately connected mathematically with one another by the Fourier transformation. There is no additional information contained in the spectra that is not already contained in the correlations, but the two methods of description put different emphases on different aspects of the problem. For example, we discussed earlier the concept of energy transfer between different scales or orders of eddies. Spectral analysis allows us to describe the exchange of kinetic energy associated with different eddy sizes or with different fluctuation frequencies occurring in the turbulence.

Journal ArticleDOI
TL;DR: A model of local spectral analysis of the image performed by the complex receptive fields of the visual cortex has been proposed and an essential feature of the model is that the generalized piece-wise Fourier transform is performed not over the image luminance function but over the logarithm contrast function, removing a number of experimental objections offered against the hypothesis of two-dimensional Fouriertransform in the visual system.
Abstract: On the basis of experimental evidence presented earlier a model of local spectral analysis of the image performed by the complex receptive fields of the visual cortex has been proposed. An essential feature of the model is that the generalized piece-wise Fourier transform is performed not over the image luminance function but over the logarithm contrast function resulted from analysis of the image by the round receptive fields of the preceding levels. Such an assumption removes a number of experimental objections offered against the hypothesis of two-dimensional Fourier transform in the visual system. The consequencies from the piece-wise expansion in a series of basic functions have been considered and among them: the channel frequency characteristics which can have more than one maximum; the possibility of describing the image by a limited number of channels with overlapping frequency characteristics; the existence of mechanisms for estimation of phase shift between frequencies.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the multiplex advantage cannot be realized to a numerical extent equal to the square root of the number of independent spectral elements in broad featureless spectra such as are used to measure specimen transmission.

Journal ArticleDOI
TL;DR: In this paper, the authors discuss the signal/noise ratios attainable in Fourier transform infrared (FT-IR) spectroscopy, including the magnitude of the multiplex and throughput advantages.
Abstract: There has been considerable discussion about the signal/noise ratios attainable in Fourier transform infrared (FT-ir) spectroscopy. This involves not only the magnitude of the multiplex and throughput advantages of FT-ir, but also several other features of this technology.

Journal ArticleDOI
TL;DR: In this paper, the shape and smoothness of a spectral density matrix were incorporated into the formation of a spectral estimate using a conjugate prior distribution, which is a product of inverted gamma distributions.
Abstract: SUMMARY This paper considers the problem of incorporating prior information about the shape and smoothness of a spectral density into the formation of a spectral estimate. Two types of finite dimensional parameters are considered, the spectral ordinates at a specified collection of frequencies and the amount of power in each of a set of frequency bands. A method which is conditional on the asymptotic distribution of periodogram averages is proposed. A formal procedure applies Bayes's theorem. A conjugate prior distribution is a product of inverted gamma distributions. The results extend to estimation of a spectral density matrix in the vector case.

Journal ArticleDOI
01 Jun 1977
TL;DR: A trick permits the use of several aliased fast Fourier transforms in place of a single unambiguous f.f.t. if the proportion of active spectral lines, or directions of arrival, is well under 1%, their location, but not the amplitude, can be computed with a dramatically reduced workload.
Abstract: A trick permits the use of several aliased fast Fourier transforms (f.f.t.) in place of a single unambiguous f.f.t. If the proportion of active spectral lines, or directions of arrival, is well under 1%, their location, but not the amplitude, can then be computed with a dramatically reduced workload.




Proceedings ArticleDOI
01 May 1977
TL;DR: An elegant method of obtaining the Arcsine transform and its application to several important signal processing problems are discussed, among them computation of discrete Fourier transforms and correlation functions, realization of digital filters, modulation and detection of signals, and construction of frequency synthesizers.
Abstract: By initially transforming a signal into its Arcsine value, the multiplications required in the subsequent processing of the signal can be replaced by additions and table look-ups. With the advent of large read-only memories, this may be an attractive method to reduce computation time and simplify hardware in signal processing systems. An elegant method of obtaining the Arcsine transform and its application to several important signal processing problems are discussed. Among these are computation of discrete Fourier transforms and correlation functions, realization of digital filters, modulation and detection of signals, and construction of frequency synthesizers.

Proceedings ArticleDOI
01 May 1977
TL;DR: In this article, the side-lobe structure of MEM spectra is studied, and a link between MEM and ML spectrum estimates is derived, which allows a clear explanation for the smoothing in ML spectra.
Abstract: This presentation treats three aspects of high resolution spectral estimation - firstly the side-lobe structure of MEM spectra is studied, next a link between MEM and ML spectrum estimates is derived, which allows a clear explanation for the smoothing in ML spectra, and finally an approach is proposed for designing an iterative scheme to estimate the spectrum of an ARMA process.


01 Jan 1977
TL;DR: In this article, a collection of technical reports dealing with estimation of spectra of stationary processes, both by the now-standard direct approach and by the more recent autoregressive approach, is presented.
Abstract: : This collection of technical reports deals with estimation of spectra of stationary processes, both by the now-standard direct approach and by the more recent autoregressive approach. The topics range over numerical procedures involving Fast Fourier Transforms, cross-spectral estimation, minimum bias windows, vernier FFTs, coherence, univariate and multivariate maximum entropy spectral estimation, and probability distributions special estimates. These results, which were new when published, are still of great relevance to anyone doing spectral analysis who is interested in obtaining good resolution and stability from limited record lengths. Partial Contents: Alternate Forms and Computational Considerations for Numerical Evaluation of Cumulative Probability Distributions Directly from Characteristic Functions; Spectral Estimation by Means of Overlapped Fast Fourier Transform Processing of Windowed Data; An Approximate Fast Fourier Transform Technique for Vernier Spectral Analysis; Approximation for Statistics of Coherence Estimators; Spectral Analysis of a Univariate Process With Bad Data Points, Via Maximum Entropy and Linear Predictive Techniques; FORTRAN Program for Multivariate Linear Predictive Spectral Analysis, Employing Forward and Backward Averaging; and FORTRAN Program for Linear Predictive Spectral Analysis of a Complex Univariate Process.