Showing papers on "Spectral density estimation published in 1986"

Fringe-pattern analysis using a 2-D Fourier transform

Abstract: A refinement of the Fourier transform fringe-pattern analysis technique which uses a 2-D Fourier transform is described. The 2-D transform permits better separation of the desired information components from unwanted components than a 1-D transform. The accuracy of the technique when applied to real data recorded by a system with a nonlinear response function is investigated. This leads to simple techniques for optimizing an interferogram for analysis by these Fourier transform methods and to an estimate of the error in the retrieved fringe shifts. This estimate is tested on simulated data and found to be reliable.

Adaptive comb filtering for harmonic signal enhancement

Abstract: A new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise. The algorithm is composed of two cascaded parts. The first estimates the fundamental frequency and enhances the harmonic component in the input, and the second estimates the harmonic amplitudes and phases. Performance analysis provides new results for the asymptotic Cramer-Rao bound (CRB) on the parameters of harmonic signals with additive white noise. Results of simulations indicate that the variances of the estimates are of the same order of magnitude as the CRB for sufficiently large data sets, and illustrate the performance in enhancing noisy artificial periodic signals.

Estimation of Signal Parameters via Rotational Invariance Techniques - ESPRIT

Abstract: A new approach to the general problem of signal parameter estimation is described. Though the technique (ESPRIT) is discussed in the context of direction-of-arrival estimation, it can be applied to a wide variety of problems including spectral estimation. ESPRIT exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure (e.g., pairwise matched and co-directional antenna element doublets) and has several advantages over earlier techniques such as MUSIC including improved performance, reduced computational load, freedom from array characterization/calibration, and reduced sensitivity to array perturbations. Results of computer simulations carried out to evaluate the new algorithm are presented.

Modeling the noise influence on the Fourier coefficients after a discrete Fourier transform

Abstract: An analysis is made to study the influence of time-domain noise on the results of a discrete Fourier transform (DFT). It is proven that the resulting frequency-domain noise can be modeled using a Gaussian distribution with a covariance matrix which is nearly diagonal, imposing very weak assumptions on the noise in the time domain.

Adaptive spectral estimation by the conjugate gradient method

Abstract: This paper proposes an alternative technique for adaptive spectral estimation. The new technique applies the method of conjugate gradient, which is used for iteratively finding the generalized eigenvector corresponding to the minimum generalized eigenvalue of a semidefinite Hermitian matrix, to the adaptive spectral analysis problem. Computer simulations have been performed to compare the new method to existing ones. From the limited examples presented, it is seen that the new method is computationally more efficient at the expense of more core storage. Also, this method is effective for small data records and can implement noise correction to yield unbiased spectral estimates if an estimate of the noise covariance matrix is available. The technique performs well for both narrow-band and wide-band signals.

Estimation Of Signal Parameters Via Rotational Invariance Techniques - ESPRIT

Abstract: A novel approach to the general problem of signal parameter estimation is described. Though the technique (ESPRIT) is discussed in the context of direction-of-arrival estimation, it can be applied to a wide variety of problems including spectral estimation. ESPRIT exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure (e.g., pairwise matched and co-directional antenna element doublets). The new approach has several significant advantages over earlier techniques such as MUSIC including improved performance, reduced computational load, freedom from array characterization/calibration, and reduced sensitivity to array perturbations. Results of computer simulations carried out to evaluate the new algorithm are presented.

A recursive estimation algorithm using selective updating for spectral analysis and adaptive signal processing

Abstract: This correspondence presents a recursive estimation algorithm which, unlike conventional ones, updates the estimates only when a sufficient improvement can be obtained. With a bounded noise, assumption, the resulting sequence of estimates is a sequence of convex sets (ellipsoids) in the parameter space. For the cases studied, the algorithm used less than 20 percent of the data to update the estimates and still acquired very good accuracy for spectral estimation.

LPZ spectral analysis using linear prediction and the z transform

Abstract: A new method of spectral analysis that combines linear prediction and z‐transform, the LPZ is described. LPZ is compared with the fast Fourier transform FFT method of data analysis. The superior frequency resolution and sensitivity and the noise reduction is described when LPZ is used in spectral analysis. (AIP)

A noise-compensated long correlation matching method for AR spectral estimation of noisy signals

Abstract: A noise-compensated long correlation matching (NCLCM) method is proposed for autoregressive (AR) spectral estimation of the noisy AR signals. This method first computes the AR parameters from the high-order Yule-Walker equations. Next, it employs these AR parameters and uses the low-order Yule-Walker equations to compensate the zeroth autocorrelation coefficient for the additive white noise. Finally, it solves the low- as well as high-order Yule-Walker equations in a least-squares sense to determine the AR parameters. It is shown that for the noisy AR signals the NCLCM method performs better than the conventional Burg method and the high-order Yule-Walker method.

Method for measuring a signal's frequency components

Abstract: A method is presented for accurately measuring an input signal's frequency components and the amplitude of those components. This is done by digitizing an input signal, passing it through a window, converting it into the frequency domain, and using the Fourier transform of the window to remove the effects of window from the input signal converted into the frequency domain.

High resolution spectral estimation of sinusoids in colored noise using a modified Pisarenko decomposition

Abstract: A method of recovering sinusoids from additive arbitrary colored noise is presented It was a Hankel matrix formulation to recover the frequencies, and reduces to the Pisarenko decomposition for the case of white noise

The kepstrum method for spectral analysis

Abstract: The Fourier transform of the logarithm of spectral density is a useful tool for spectral analysis of random signals which are highly resonant. This is because the logarithm compresses the large peaks of the spectrum and a resulting power series expansion (kepstrum) can be truncated at a suitable length to suppress the higher frequencies. This paper utilizes the FFT in a similar form in order to obtain spectral smoothing. Several examples show the advantages of the method including an analysis on the pitch and roll data of a container ship. It is also shown how a smooth frequency response (Bode plot) can be found to identify the signal generating process. This technique is extended to systems with signal plus noise and the identification then becomes equivalent to spectral factorization, a technique particularly useful in the determi nation of Kalman filters.

Method and apparatus for identifying the components of a signal

Abstract: Fast Fourier Transform methods of analysing signal frequencies spectra yield results from zero frequencies upwards. Thus, when the frequency band of interest is not at very low frequencies a lot of wasted calculations may be performed, and resolution and computation time have to be traded-off against each other, often falling short of the requirements for both. A technique is described in which the signal to be analysed is passed through an anti-alias filter and initial transform data is collected by undersampling. In a railway track circuit receiver which is to identify a predetermined carrier frequency or FSK signal, the anti-alias filter is selected to exclude frequencies other than those in a frequency band including the particular track signal so that there is no ambiguity in the calculated transform results.

Spectral decomposition and extrapolation of variations in electricity loading

Abstract: The possibility of using a frequency domain approach to forecasting short, medium and long term electricity consumption data is discussed in the paper. In particular, a new super-resolution spectral estimation technique allows for the decomposition of the variations in such data about selected trends and extrapolation beyond the limits of the original data. It is shown that for short- and medium-term data, the frequency components present appear harmonically related and in phase, but a stationarity problem exists for the long-term data, preventing useful forecasts being made. However, the technique does appear to be a possible alternative to the more traditional time-domain approaches.

Parametric spectral estimation for arma processes

Abstract: "IEEE Thrid ASSP Workshop on Spectrum Estimation and Modeling, Boston, MA, November 17-18, 1986."

A singular-value decomposition approach to X-ray spectral estimation from attenuation data

Abstract: A singular-value decomposition (SVD) approach is described for estimating the exposure-rate spectral distributions of X-rays from attenuation data measured with various filtrations. This estimation problem with noisy measurements is formulated as the problem of solving a system of linear equations with an ill-conditioned nature. The principle of the SVD approach is that a response matrix, representing the X-ray attenuation effect by filtrations at various energies, can be expanded into summation of inherent component matrices, and thereby the spectral distributions can be represented as a linear combination of some component curves. A criterion function is presented for choosing the components needed to form a reliable estimate. The feasibility of the proposed approach is studied in detail in a computer simulation using a hypothetical X-ray spectrum. The application results of the spectral distributions emitted from a therapeutic X-ray generator are shown. Finally some advantages of this approach are pointed out.

Performance of multichannel autoregressive spectral estimators

Abstract: This paper compares and contrasts the performance of multichannel periodogram and autoregressive spectrum analysis techniques periodogram when processing sunspot and world air temperature data, a first order autoregressive process, and an artificial data set of sinusoids in colored noise. It is shown that the high resolution benefit of autoregressive analysis must be tempered by an awareness of a severe feed across effect among the autospectral autoregressive estimates that may prevent multichannel autoregressive spectral estimation from being a viable spectral estimation approach. The feed across effect manifests itself as very sharp spikes in the autospectrum where there should be no spectral energy. The cause is known to be inexact pole-zero cancellation in the autoregressive coeffieient matrix estimates. Performing single channel autoregressive spectral estimates will provide indications of where the feed across effect is occurring. The astronomical literature has applied these multichannel autoregressive techniques to correlate sunspot activity with terrestrial activity such as tides, earth rotation variations, air temperature variations, and drought cycles. High correlation has alledgedly been found. However, the findings of the literature is now in doubt because this author believes that the astrophysical researchers were misled by the feed across anomaly. This paper also serves to correct some errors reported on examples in reference [3].

Accuracy of angular spectral analysis with an anamorphic Fourier transformer

Abstract: Angular measurements in symmetrical and nonsymmetrical Fourier spectra are compared. The coefficient of angular magnification of a spectrum and the effective angular extent of a scanning wedge filter are introduced. Better accuracy of angular spectral analysis with an anamorphic Fourier transformer is explained and experimentally proved.

On the Accuracy of Omega Diagnostic Computations

Abstract: The accuracies of algorithms used to compute quasi-geostrophic diagnostic parameters such as Hoskins' Q-vector and its divergence are evaluated. Analytically-determined height values are invoked at grid points representing three pressure surfaces, and finite difference approximations to third and lower order derivatives are compared with analytic values. Errors from these approximations are found to be virtually identical to those predicted by a mathematical analysis of the centered difference scheme. The magnitudes of finite difference errors are a function of wavelength, being acceptably small for waves sampled nine or more times per wavelength. Interpolation of grid point values from analytically determined observations at a typical array of rawinsonde stations produces diagnostic results that, while they contain many distortions owing mainly to data sparseness still contain significant portions of the signal, as determined by a two-dimensional spectral estimation technique using Fourier analy...

Doppler signal analyzing apparatus

Abstract: A Doppler signal analyzing apparatus is capable of frequency analysis of a Doppler signal with frequency and time resolutions that match the frequency band of a signal to be analyzed. The signal to be analyzed is divided into a plurality of frequency bands by bandpass means (10 1 , 10 2 , 10 3 ), and signals in the frequency bands which have passed through the bandpass means are acquired by signal acquiring means (11) over time slots that are smaller for higher-frequency signals and larger for lower-frequency signals. The signals acquired by the signal acquiring means are subjected to a Fourier transform by Fourier transform means (14).

Frequency identification by complex spectrum

Abstract: The fundamental frequency of signal is one of the important information. We can obtain the frequency of periodic wave from the peak of spectrum calculated by FFT. But the resolution of peak frequency is not so high. To get higher resolution, some methods have been proposed. They require a great deal of calculation. To improve the calculation speed, this paper proposes a new method to estimate the fundamental frequency in short observation interval using the complex spectrum. The phase component of complex spectrum gives us a useful information to increase the resolution. Using the characteristics of complex spectrum, we obtained the peak frequency with negligible error. This method requires a little caliclation. The frequency of signal can be estimated in real time when an array processor is used.

Apparatus for performing a fast fourier transform

Abstract: In a railway vehicle safety system, a frequency modulated signal is transmitted to a vehicle informing, inter alia, of a safe maximum speed, the said speed being represented by the carrier modulation frequency. In addition, the frequency of the carrier may possess one of a number of alternative frequencies. Apparatus for analysing received signals to identify the carrier frequency and the modulation frequency employs a fast Fourier transform processor. In order to save computation time by eliminating useless calculations, a received signal is heterodyned by a local signal selected according to the carrier frequency identified and the base-band components are analysed to identify the modulation frequency. A first stage transform is performed to identify the carrier signal and select the local signal frequency for a complex heterodyne process in a second stage in which local signals in phase quadrature are mixed with the received signal and the results sampled to provide data for real and imaginary data arrays for the transform process. As a result of the second stage process, noise and common mode interference signals are rejected.