Showing papers on "Spectral density estimation published in 1994"

Sensorless speed measurement using current harmonic spectral estimation in induction machine drives

Abstract: This paper proposes a sensorless speed measurement scheme which improves the performance of transducerless induction machine drives, especially for low frequency operation. Speed-related harmonics which arise from rotor slotting and eccentricity are analyzed using digital signal processing. These current harmonics exist at any nonzero speed and are independent of time-varying parameters such as stator winding resistance. A spectral estimation technique combines multiple current harmonics to determine the rotor speed with more accuracy and less sensitivity to noise than analog filtering methods or the fast Fourier transform. An on-line initialization routine determines machine-specific parameters required for slot harmonic calculations. This speed detector, which has been verified at frequencies as low as 1 Hz, can provide robust, parameter-independent information for parameter tuning or as an input to a sensorless flux observer for a field-oriented drive. The performance of the algorithm is demonstrated over a wide range of inverter frequencies and load conditions. >

A fast spectral estimation algorithm based on the FFT

Abstract: A simple FFT-based algorithm for spectrum estimation is presented. The major difference between this and spectrum estimation using a single pass through the FFT is that the proposed algorithm is iterative and the FFT is used many times in a systematic may to search for individual spectral lines. Using simulated data, the proposed algorithm is able to detect mulitple sinusoids in additive noise. The algorithm is certainly better than the single pass FFT in separating closely spaced sinusoids. Finally the algorithm is applied to some experimental measurements to illustrate its properties. >

Nonparametric Spectral Density Estimation Using Penalized Whittle Likelihood

Abstract: The penalized likelihood approach is not well developed in time series analysis, even though it has been applied successfully in a number of nonparametric function estimation problems. Chow and Grenander proposed a penalized likelihood-type approach to the nonparametric estimation of the spectral density of Gaussian processes. In this article this estimator is extended to more general stationary processes, its practical implementation is developed in some detail, and some asymptotic rates of convergence are established. Its performance is also compared to more widely used alternatives in the field. A computational algorithm involving an iterative least squares, initialized by the log-periodogram, is first developed. Then, motivated by an asymptotic linearization, an estimator of the integrated squared error between the estimated and true log-spectral densities is proposed. From this, a data-dependent procedure for selection of the amount of smoothing is constructed. The methodology is illustrated...

Frequency analysis method

Abstract: A frequency analysis method comprises using a window function to evaluate aemporal input signal present in the form of discrete sampled values. The windowed input signal is subsequently subjected to Fourier transformation for the purpose of generating a set of coefficients. In order to develop such a method so that the characteristics of the human ear are simulated not only with respect to the spectral projection in the frequency range, but also with respect to the resolution in the temporal range, a set of different window functions is used to evaluate a block of the input signal in order to generate a set of blocks, weighted with the respective window functions, of sampled values whose Fourier transforms have different bandwidths, before each of the simultaneously generated blocks of sampled values is subjected to a dedicated Fourier transformation in such a way that for each window function at least respectively one coefficient is calculated which is assigned the bandwidth of the Fourier transforms of this window function, and that the coefficients are chosen such that the frequency bands assigned to them essentially adjoin one another.

Sidelobe reduction via adaptive FIR filtering in SAR imagery

Abstract: The paper describes a class of adaptive weighting functions that greatly reduce sidelobes, interference, and noise in Fourier transform data By restricting the class of adaptive weighting functions, the adaptively weighted Fourier transform data can be represented as the convolution of the unweighted Fourier transform with a data adaptive FIR filter where one selects the FIR filter coefficients to maximize signal-to-interference ratio This adaptive sidelobe reduction (ASR) procedure is analogous to Capon's (1969) minimum variance method (MVM) of adaptive spectral estimation Unlike MVM, which provides a statistical estimate of the real-valued power spectral density, thereby estimating noise level and improving resolution, ASR provides a single-realization complex-valued estimate of the Fourier transform that suppresses sidelobes and noise Further, the computational complexity of ASR is dramatically lower than that of MVM, which is critical for large multidimensional problems such as synthetic aperture radar (SAR) image formation ASR performance characteristics can be varied through the choice of filter order, l/sub 1/- or l/sub 2/-norm filter vector constraints and a separable or nonseparable multidimensional implementation The author compares simulated point scattering SAR imagery produced by the ASR, MVM, and MUSIC algorithms and illustrates ASR performance on three sets of collected SAR imagery >

Special problems in the estimation of power-law spectra as applied to topographical modeling

Abstract: An increasing number of topographical studies find that natural surfaces possess power-law roughness spectra. Power-law spectra introduce unique difficulties in the spectral estimation process. The authors describe how an improper window choice allows leakage that yields a spectral estimate that is insensitive to the spectral slope. In addition, the commonly used Fourier-based spectral estimates have higher variances than other available estimators. Higher variance is particularly problematic when data records are short, as is often the case in remote sensing studies. The authors show that Capon's spectral estimator has less variance than Fourier-based estimators and measures the spectral slope more accurately. The authors also show how estimates of a 2D roughness spectrum can be obtained from estimates of the 1D spectrum for the isotropic power-law case. >

The variance of multitaper spectrum estimates for real Gaussian processes

Abstract: Multitaper spectral estimation has proven very powerful as a spectral analysis method wherever the spectrum of interest is detailed and/or varies rapidly with a large dynamic range. In his original paper D.J. Thomson (1982) gave a simple approximation for the variance of a multitaper spectral estimate which is generally adequate when the spectrum is slowly varying over the taper bandwidth. The authors show that near zero or Nyquist frequency this approximation is poor even for white noise and derive the exact expression of the variance in the general case of a stationary real-valued time series. This expression is illustrated on an autoregressive time series and a convenient computational approach outlined. It is shown that this multitaper variance expression for real-valued processes is not derivable as a special case of the multitaper variance for complex-valued, circularly symmetric processes, as previously suggested in the literature. >

Radar system with adaptive clutter suppression

Abstract: A method of spectral estimation of a received radar signal wherein an image of the received radar signal is applied to windows of differing prolate spheroidal sequences to calculate multiple eigenspectra. The value of each of said sequences are multiplied with the radar signal, and the Fourier transforms of the products provide a plurality of realizations of orthogonal eigenspectra. The orthogonal eigenspectra are combined into a minimum variance, low bias estimate of the mean power spectrum and an estimate of a variance of said spectrum for each frequency in the spectrum to provide a more accurate estimate of back ground noise and to further improve detection performance.

Development and analysis of a neural network approach to Pisarenko's harmonic retrieval method

Abstract: Pisarenko's harmonic retrieval (PHR) method is perhaps the first eigenstructure based spectral estimation technique. The basic step in this method is the computation of eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix of the underlying data. The authors recast a known constrained minimization formulation for obtaining this eigenvector into the neural network (NN) framework. Using the penalty function approach, they develop an appropriate energy function for the NN. This NN is of feedback type with the neurons having sigmoidal activation function. Analysis of the proposed approach shows that the required eigenvector is a minimizer (with a given norm) of this energy function. Further, all its minimizers are global minimizers. Bounds on the integration time step that is required to numerically solve the system of nonlinear differential equations, which define the network dynamics, have been derived. Results of computer simulations are presented to support their analysis. >

High resolution ultrasonic backscatter coefficient estimation based on autoregressive spectral estimation using Burg's algorithm

Abstract: An autoregressive (AR) method for spectral estimation was applied toward the task of estimating ultrasonic backscatter coefficients from small volumes of tissue. High spatial resolution is desirable for generating images of backscatter coefficient. Data was acquired from a homogeneous tissue-mimicking phantom and from a normal human liver in vivo. The AR method was much more resistant to gating artifacts than the traditional DFT (discrete Fourier transform) approach. The DFT method consistently underestimated backscatter coefficients at small gate lengths. Therefore backscatter coefficient image formation will be quantitatively more meaningful if based on AR spectral estimation rather than the DFT. The autoregressive method offers promise for enhanced spatial resolution and accuracy in ultrasonic tissue characterization and nondestructive evaluation of materials. >

Short-time Fourier transform and wavelet transform with Fourier-domain processing

Abstract: We discuss the semicontinuous short-time Fourier transform (STFT) and the semicontinual wavelet transform (WT) with Fourier-domain processing, which is suitable for optical implementation. We also systematically analyze the selection of the window functions, especially those based on the biorthogonality and the orthogonality constraints for perfect signal reconstruction. We show that one of the best substitutions for the Gaussian function in the Fourier domain is a squared sinusoid function that can form a biorthogonal window function in the time domain. The merit of a biorthogonal window is that it could simplify the inverse STFT and the inverse WT. A couple of optical architectures based on Fourier-domain processing for the STFT and the WT, by which real-time signal processing can be realized, are proposed.

Multifrequency Doppler: improving the quality of spectral estimation by making full use of the information present in the backscattered RF echoes

Abstract: This paper investigates the application of the two-dimensional Fourier transform in the context of pulsed wave Doppler. It is shown that two-dimensional spectral analysis of the backscattered RF echoes provides individual Doppler spectra corresponding to the whole range of transmitted frequencies which can be combined, after proper scaling, to form a "multifrequency" spectral estimate. Theoretical expressions are derived for the signal-to-noise ratio of the multifrequency sonogram which predict substantial gains over the conventional (one-dimensional) approach for Doppler processing. These predictions are verified by means of extensive simulations, which also provide an insight into the effect of electronic noise. >

Eigen-based Doppler estimation for differentially coherent CPM

Abstract: Eigen-based methods are developed for obtaining fast and accurate Doppler estimates in both land-mobile satellite and urban microcellular applications. By showing that the correlations of a set of differentially processed CPM signals have the same form as the autocorrelations of a complex exponential in noise, eigen-based spectral estimation techniques are used to provide improved Doppler estimates in noise. The eigen-based Doppler estimators are shown to have significantly less variance and mean square error than previously proposed Doppler estimators that use only simple averaging. >

Comparison of the performance of three maximum doppler frequency estimators coupled with different spectral estimation methods

Abstract: The performance of three spectral techniques (FFT, AR Burg and ARMA) for maximum frequency estimation of the Doppler spectra is described. Different definitions of fmax were used: frequency at which spectral power decreases down to 0.1 of its maximum value, modified threshold crossing method (MTCM) and novel geometrical method. "Goodness" and efficiency of estimators were determined by calculating the bias and the standard deviation of the estimated maximum frequency of the simulated Doppler spectra with known statistics. The power of analysed signals was assumed to have the exponential distribution function. The SNR ratios were changed over the range from 0 to 20 dB. Different spectrum envelopes were generated. A Gaussian envelope approximated narrow band spectral processes (P. W. Doppler) and rectangular spectra were used to simulate a parabolic flow insonified with C. W. Doppler. The simulated signals were generated out of 3072-point records with sampling frequency of 20 kHz. The AR and ARMA models order selections were done independently according to Akaike Information Criterion (AIC) and Singular Value Decomposition (SVD). It was found that the ARMA model, computed according to SVD criterion, had the best overall performance and produced results with the smallest bias and standard deviation. In general AR(SVD) was better than AR(AIC). The geometrical method of fmax estimation was found to be more accurate than other tested methods, especially for narrow band signals.

A procedure for oscillatory parameter identification

Abstract: A procedure is proposed where a power system is excited with a low-level pseudo-random probing signal and the frequency, damping, magnitude, and shape of oscillatory modes are identified using spectral density estimation and frequency-domain transfer function identification. Attention is focussed on identifying system modes in the presence of noise. Two example cases are studied: identification of electromechanical oscillation modes in a 16-machine power system; and turbine-generator shaft modes of a 3-machine power plant feeding a series-compensated 500-kV network. >

Method and apparatus for enhancing frequency domain analysis

Abstract: A signal processing technique allows accurate interpolation between points of a sampled frequency domain function. A time-based sampling process samples a time waveform of duration T having a sub time interval T'. A signal processor applies a discrete Fourier transform over a time period T to transform the sampled data from the time domain to the frequency domain. The sampled frequency domain data is convolved with one or more convolution kernels to yield a continuous line shape. The result of this convolution permits the spectral composition at arbitrary frequencies to be determined. The disclosed frequency domain interpolation process is characterized by preservation of data in the T' interval of the time domain with an arbitrary but specified degree of accuracy.

Quadratic time-varying spectral estimation for underspread processes

Abstract: We study time-varying spectral estimation for nonstationary processes with restricted time-frequency (TF) correlation. We present explicit bias and variance expressions for quadratic TF-invariant (QTFI) estimators of an expected real-valued QTFI representation based on a single noisy observation. Unbiased theoretical estimators with globally minimal variance are derived and approximately realized by a matched multiwindow method. >

A procedure for oscillatory parameter identification

Abstract: A procedure is proposed where a power system is excited with a low-level pseudo-random probing signal and the frequency, damping, magnitude, and shape of oscillatory modes are identified using spectral density estimation and frequency-domain transfer function identification. Attention is focussed on identifying system modes in the presence of noise. Two example cases are studied: identification of electromechanical oscillation modes in a 16-machine power system; and turbine-generator shaft modes of a 3-machine power plant feeding a series-compensated 500-kV network. >

Adaptive weak signal identification system

Abstract: An adaptive weak signal identification system having a simple implementation which is capable of rapidly tracking weak signals with time varying frequencies in the presence of a strong interference signal. The system includes a first Fast Fourier Transform circuit for performing a Fast Fourier Transform on a discrete block of data points of an input data signal. A filter coefficient generator is coupled to the output of the Fast Fourier Transform circuit, and identifies the frequency of the strong interference signal, and then based thereon generates filter coefficients for a notch filter. A notch filter receives the generated filter coefficients, and further has the input data signal as an input, on which it performs a notch filtering operation to dramatically reduce the intensity of the interference signal. A second Fast Fourier Transform circuit then performs a Fast Fourier Transform on the output passed by the notch filter, and the output of the Fast Fourier Transform circuit is analyzed to identify the frequency of the weak signal of interest.

A novel technique for narrowband/broadband interference excision in DS-SS communications

Abstract: A novel technique for narrowband/broadband frequency selective limiting in direct sequence-spread spectrum (DS-SS) communications is presented. This technique relies on setting the magnitude response of the received signal Fourier transform to a predetermined function while leaving the phase response unchanged. When the Fourier transform magnitude response of the signal is made constant over the entire signal spectrum, this nonlinear processor will operate as a whitening filter. >

Autoregressive (AR) and autoregressive moving average (ARMA) spectral estimation techniques for faster TLM analysis of microwave structures

Abstract: Autoregressive (AR) and autoregressive moving average (ARMA) techniques have been successfully implemented in conjunction with the transmission line matrix (TLM) method for efficient time-domain analysis of microwave structures. The AR technique can be used to compute the full time-domain response from a relatively short segment of the early TLM response. It was found that the least-square technique of estimating the AR parameters requires a shorter time record than solving Yule-Walker equations through the Levinson-Durbin algorithm. The ARMA technique can be used to compute the scattering parameters of microwave structures without using the discrete Fourier transform. A recursive least square covariance ladder algorithm has been used for ARMA modeling. Both AR and ARMA models have been validated by applying them to waveguide and suspended substrate stripline filters. With these techniques, the speed of the computationally intensive TLM algorithm can be increased up to five times. >

Spectral estimation of plasma fluctuations. I. Comparison of methods

Abstract: The relative root mean squared errors (RMSE) of nonparametric methods for spectral estimation is compared for microwave scattering data of plasma fluctuations. These methods reduce the variance of the periodogram estimate by averaging the spectrum over a frequency bandwidth. As the bandwidth increases, the variance decreases, but the bias error increases. The plasma spectra vary by over four orders of magnitude, and therefore, using a spectral window is necessary. The smoothed tapered periodogram is compared with the adaptive multiple taper methods and hybrid methods. It is found that a hybrid method, which uses four orthogonal tapers and then applies a kernel smoother, performs best. For 300 point data segments, even an optimized smoothed tapered periodogram has a 24% larger relative RMSE than the hybrid method. Two new adaptive multitaper weightings which outperform Thomson’s original adaptive weighting are presented.

Spectral estimation of radar time-of-arrival periodicities

Abstract: Disclosed is a method to extract the periodic properties (or Pulse Repetition Intervals (PRIs)) of radar signals whose time-of-arrival at an airborne platform have been time tagged by an Electronic Warfare (EW) receiver. The PRIs are determined using a modified Discrete Fourier Transform (DFT) written as ##EQU1## where k represents the frequency components, the Ti are the individual Time-Of-Arrival (TOA) data values and N is the last TOA value collected. Disclosed are three possible methods of reducing the number of computations involved with the modification of the Discrete Fourier Transform (DFT) equation to facilitate its use with Radar Time-Of-Arrival (TOA) to extract periodic properties of radar signals. This is particularly applicable to radar pulse trains which are interleaved in time and where each individual pulse train may be staggered or jittered in time so that a time domain deinterleaving scheme must be employed. A spectral estimator can be computed by taking the modulus of the DFT of the time series data and extending the periodogram estimator by making a slight modification of the DFT equation.

A review of advanced methods for simulation output analysis

Abstract: Reviews statistical methods for analyzing output data from computer simulations of single systems. In particular, this paper focuses on the problems of choosing initial conditions and estimating steady-state system parameters. The estimation techniques include the replication/deletion approach, the regenerative method, the batch means method, the standardized time series method, the autoregressive method, and the spectral estimation method.

Improved musical pitch tracking using principal decomposition analysis

Abstract: We present a technique for improving the performance of a method for estimating the time-varying fundamental frequency (pitch) of a musical signal corrupted by interference components. The original method, developed by M. Piszczalski and B.A. Galler (1979), involves the calculation and comparison of frequency-pair ratios from each spectrum within a time-frequency transform of the corrupted signal. As the strength of the interference components is increased, the frequency estimates from this method become more unreliable. To obtain improved performance we developed a transform conditioning procedure that enhances the harmonic signal's spectral components in a constant-Q transform prior to the calculation of frequency-pair ratios. This transform conditioning technique is based on a method we have previously developed for principal decomposition analysis of time-frequency transforms. >

Wavenumber Spectrum of Very Short Wind Waves: An Application of Two-Dimensional Slepian Windows to Spectral Estimation

Abstract: A multitaper 2D spectral estimation method is developed for increasing the degree of freedom of the estimation. The core of this method is 2D Slepian eigen windows that are optimum in the sense of minimizing the spectral leakage. Wavenumber spectra of very short wind wave slopes are calculated by this method. The advantages of the multitaper technique are shown by obtaining smooth wavenumber spectra from a limited amount of image data. The data used for the spectral estimation were measured in the laboratory with a water surface gradient detector developed by the authors. Important features of the spatial distribution of short-wave energy are newly revealed. The widening of angular spreading of energy density spectra is not monotonic with increasing wave-number. There is a local plat region of minimum angular spreading in the spectral band of parasitic capillary waves that suggests that there is another upstream of energy cascade in spite of the energetic gravity-wave spectral peak. The input ene...