Showing papers on "Spectral density estimation published in 2000"

A new approach to spectral estimation: a tunable high-resolution spectral estimator

Abstract: Traditional maximum entropy spectral estimation determines a power spectrum from covariance estimates. Here, we present a new approach to spectral estimation, which is based on the use of filter banks as a means of obtaining spectral interpolation data. Such data replaces standard covariance estimates. A computational procedure for obtaining suitable pole-zero (ARMA) models from such data is presented. The choice of the zeros (MA-part) of the model is completely arbitrary. By suitable choices of filter bank poles and spectral zeros, the estimator can be tuned to exhibit high resolution in targeted regions of the spectrum.

System design for accurately estimating the spectral reflectance of art paintings

Abstract: Accurately estimating the spectral reflectance of art paintings from low-dimensional multichannel images requires that both image-acquisition hardware with appropriate spectral characteristics and appropriate estimation software be applied to the captured multichannel image. In this study, a system that incorporates both factors is designed and developed on the basis of the minimum-mean-square error criterion. The accuracy of spectral estimation by use of this system is evaluated, and the system's high performance is demonstrated.

Improved heart rate variability signal analysis from the beat occurrence times according to the IPFM model

Abstract: The heart rate variability (HRV) is an extended tool to analyze the mechanisms controlling the cardiovascular system. In this paper, the integral pulse frequency modulation model (IPFM) is assumed. It generates the beat occurrence times from a modulating signal. This signal is thought to represent the autonomic nervous system action, mostly studied in its frequency components. Different spectral estimation methods try to infer the modulating signal characteristics from the available beat timing on the electrocardiogram signal. These methods estimate the spectrum through the heart period (HP) or the heart rate (HR) signal. The authors introduce a new time domain HRV signal, the Heart Timing (HT) signal. They demonstrate that this HT signal, in contrast with the HR or HP, makes it possible to recover an unbiased estimation of the modulating signal spectra. In this estimation the authors avoid the spurious components and the low-pass filtering effect generated when analyzing HR or HP.

Estimation of turbulent velocity spectra from laser Doppler data

Abstract: We review the problem of spectral estimation from velocity data sampled irregularly in time by a laser Doppler anemometer (LDA) from very early estimators based on slot correlation to more refined estimators, which build upon a signal reconstruction and an equidistant re-sampling in time. The discussion is restricted to single realization anemometry, i.e. excluding multiple particle signals. We classify the techniques and make an initial assessment before describing currently used methods in more detail. An intimately related subject, the simulation of LDA data, is then briefly reviewed, since this provides a means of evaluating various estimators. Using the expectation and variance as figures of merit, the advantages and disadvantages of several estimators for varying types of turbulent velocity spectral distributions are discussed. A set of recommendations is put forward as a conclusion.

Direct strain estimation in elastography using spectral cross-correlation.

Abstract: Spectral estimation of tissue strain has been performed previously by using the centroid shift of the power spectrum or by estimating the variation in the mean scatterer spacing in the spectral domain. The centroid shift method illustrates the robustness of the direct, incoherent strain estimator. In this paper, we present a strain estimator that uses spectral cross-correlation of the pre- and postcompression power spectrum. The centroid shift estimator estimates strain from the mean center frequency shift, while the spectral cross-correlation estimates the shift over the entire spectrum. Spectral cross-correlation is shown to be more sensitive to small shifts in the power spectrum and, thus, provides better estimation for smaller strains when compared to the spectral centroid shift. Spectral cross-correlation shares all the advantages gained using the spectral centroid shift, in addition to providing accurate and precise strain estimation for small strains. The variance and noise properties of the spectral strain estimators quantified by their respective strain filters are also presented.

Spectral Analysis and Filter Theory in Applied Geophysics

Abstract: I Spectral Analysis of Deterministic Processes.- 1 Fourier Series Representation of Periodic Functions.- 2 Spectral Representation of Nonperiodic Processes.- 3 The Dirac Delta Function and its Fourier Transform.- 4 Spectral Analysis of Time-Limited Observations of Infinitely Long Processes.- 5 Spectral Analysis of Discrete Functions.- 6 z-Transform Representation of Time Series.- 7 Examples of the Use of the Fourier Transform in Applied Seismics.- II Spectral Analysis of Random Processes.- 8 Characterization of Random Processes in the Time and Frequency Domains.- 9 Estimation of the Power Spectral Density Function.- 10 Evaluation of Magnetotelluric Survey Data.- III Spectral Analysis of Random Processes by Model Fitting.- 11 Spectral Estimation by Model Fitting.- 12 Estimating Power Spectra using Criteria from Information Theory.- IV Fundamentals of Filter Theory.- 13 Filtering from the Viewpoint of System Theory.- 14 Filtering in the Frequency Domain.- V Digital Filtering.- 15 Basics of Digital Filtering.- 16 Filtering using Simple Mathematical Operations.- 17 Designing Nonrecursive Digital Filters of Finite Length.- 18 Synthesis of Recursive Digital Filters.- VI Fundamentals of Optimum Filtering.- 19 Designing Analog and Digital Optimum Filters.- 20 Application of Optimum Filters to Reflection Seismic Data.- 21 Kalman Filters.- VII Fundamentals of Deconvolution and their Application to Reflection Seismic Data.- 22 Mathematical Basis of Deconvolution.- 23 Deconvolution: Problems and Approaches in Reflection Seismics.- VIII Multidimensional and Multichannel Filters.- 24 Multidimensional Filters.- 25 Two-Dimensional Filters for Gravity and Magnetic Data.- 26 Multichannel Filtering of Seismic Data.- Author Index.

Method and system for sub-band hybrid coding

Abstract: A system and method are provided for processing audio and speech signals using a pitch and voicing dependent spectral estimation algorithm (voicing algorithm) to accurately represent voiced speech, unvoiced speech, and mixed speech in the presence of background noise, and background noise with a single model. The present invention also modifies the synthesis model based on an estimate of the current input signal to improve the perceptual quality of the speech and background noise under a variety of input conditions. The present invention also improves the voicing dependent spectral estimation algorithm robustness by introducing the use of a Multi-Layer Neural Network in the estimation process. The voicing dependent spectral estimation algorithm provides an accurate and robust estimate of the voicing probability under a variety of background noise conditions. This is essential to providing high quality intelligible speech in the presence of background noise. In one embodiment, the waveform coding is implemented by separating the input signal into at least two sub-band signals and encoding one of the at least two sub-band signals using a first encoding algorithm to produce at least one encoded output signal; and encoding another of said at least two sub-band signals using a second encoding algorithm to produce at least one other encoded output signal, where the first encoding algorithm is different from the second encoding algorithm. In accordance with the described embodiment, the present invention provides an encoder that codes N user defined sub-band signal in the baseband with one of a plurality of waveform coding algorithms, and encodes N user defined sub-band signals with one of a plurality of parametric coding algorithms. That is, the selected waveform/parametric encoding algorithm may be different in each sub-band.

A unified view of multitaper multivariate spectral estimation

Abstract: SUMMARY The orthogonal multitaper framework for cross-spectral estimators provides a simple unifying structure for determining the corresponding statistical properties. Here crossspectral estimators are represented by a weighted average of orthogonally-tapered crossperiodograms, with the weights corresponding to a set of rescaled eigenvalues. Such a structure not only encompasses the Thomson estimators, using Slepian and sine tapers, but also Welch's weighted overlapped segment averaging estimator and lag window estimators including frequency-averaged cross-periodograms. The means, smoothing and leakage biases, variances and asymptotic distributions of such estimators can all be formulated in a common way; comparisons are made for a fixed number of degrees of freedom. The common structure of the estimators also provides a necessary condition for the invertibility of an estimated cross-spectral matrix, namely that the weight matrix of the estimator written in bilinear form must have rank greater than or equal to the dimension of the cross-spectral matrix. An example is given showing the importance of small leakage and thus illustrating that the various estimators need not be equivalent in practice.

Linear and nonlinear experimental regimes of stochastic resonance

Abstract: We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an interval of values spanning several orders of magnitude. We observe both a regime described by the linear-response theory and the nonlinear deviation from it. In the nonlinear regime we detect saturation of the power spectral density of the output signal detected at the frequency of the modulating signal and a dip in the noise level of the same spectral density. When these effects are observed we detect a phase and frequency synchronization between the stochastic output and the deterministic input.

Combining Capon and APES for estimation of spectral lines

Abstract: We propose combining the Capon and the APES spectral estimators for estimation of both the amplitude and the frequency of spectral lines. The so-obtained estimator does not suffer from Capon's biased amplitude estimates nor from APES' biased frequency estimates or resolution problem. Furthermore, the combined estimator is computationally simpler than APES and has about the same complexity as Capon. Numerical simulations are presented illustrating the increased performance.

Rotation, scale, and translation resilient public watermarking for images using a log-polar fourier transform

Abstract: A method for detecting a watermark signal in digital image data. The detecting method includes the steps of: computing a log-polar Fourier transform of the image data to obtain a log-polar Fourier spectrum; projecting the log-polar Fourier spectrum down to a lower dimensional space to obtain an extracted signal; comparing the extracted signal to a target watermark signal; and declaring the presence or absence of the target watermark signal in the image data based on the comparison. Also provided is a method for inserting a watermark signal in digital image data to obtain a watermarked image. The inserting method includes the steps of: computing a log-polar Fourier transform of the image data to obtain a log-polar Fourier spectrum; projecting the log-polar Fourier spectrum down to a lower dimensional space to obtain an extracted signal; modifying the extracted signal such that it is similar to a target watermark; performing a one-to-many mapping of the modified signal back to log-polar Fourier transform space to obtain a set of watermarked coefficients; and performing an inverse log-polar Fourier transform on the set of watermarked coefficients to obtain a watermarked image.

High-Precision Fourier Analysis of Sounds Using Signal Derivatives

Abstract: An original method is introduced which greatly improves the precision of the Fourier analysis not only in frequency and amplitude but also in time, thus minimizing the problem of the tradeoff of time versus frequency in the classic short-time Fourier transform. This method is of great interest when extracting spectral modeling parameters from existing sounds. A detailed theoretical presentation is made, and practical results obtained from implementing this method are presented.

Discrete evolutionary transform for time–frequency signal analysis

Abstract: In this paper, we introduce the discrete evolutionary transform (DET) capable of representing deterministic non-stationary signals. Besides the signal representation, the DET permits the computation of a kernel from which the evolutionary spectrum of the signal is obtained. The signal representation is modeled after the Wold–Cramer representation used for random non-stationary signals in Priestley's evolutionary spectral theory. The proposed transform generalizes the short-time Fourier transform and the spectrogram. To illustrate how to define the windows used in the DET we consider the Gabor and the Malvar cases. The Gabor-based window is time dependent and uses the bi-orthogonal analysis and synthesis windows of the expansion. The Malvar-based window is a function of time and of frequency, and depends on the orthogonal functions used in the expansion. Two types of transforms are shown: sinusoidal and chirp DETs. The sinusoidal DET represents well signals with narrow-band components, while the chirp transformation is capable of representing well signals with wide-band components provided that the instantaneous frequency information of the signal components is estimated. Examples are used to illustrate the implementation of the DET. The examples show the capability of the transform in providing excellent representation for a signal and a spectrum with very good time–frequency resolution.

Monte Carlo filtering and smoothing with application to time-varying spectral estimation

Abstract: We develop methods for performing filtering and smoothing in nonlinear non-Gaussian dynamical models. The methods rely on a particle cloud representation of the filtering distribution which evolves through time using importance sampling and resampling ideas. In particular, novel techniques are presented for generation of random realisations from the joint smoothing distribution and for MAP estimation of the state sequence. Realisations of the smoothing distribution are generated in a forward-backward procedure, while the MAP estimation procedure can be performed in a single forward pass of the Viterbi algorithm applied to a discretised version of the state space. An application to spectral estimation for time-varying autoregressions is described.

Towards a perceptually optimal spectral amplitude estimator for audio signal enhancement

Abstract: We present a statistical model-based approach to signal enhancement in the case of additive broadband noise. Because broadband noise is localised in neither time nor frequency, its removal is one of the most pervasive and difficult signal enhancement tasks. In order to improve perceived signal quality, we take advantage of human perception and define a best estimate of the original signal in terms of a cost function incorporating perceptual optimality criteria. We derive the resultant signal estimator and implement it in a short-time spectral attenuation framework.

An industrially useful means for decomposition and differentiation of harmonic components of periodic waveforms

Abstract: This paper presents efficient methods to estimate the spectral content of (noisy) periodic waveforms that are common in industrial processes The techniques presented, which are based on the recursive discrete Fourier transform, are especially useful in computing high-order derivatives of such waveforms Unlike conventional differentiating techniques, the methods presented differentiate in the frequency domain and thus are quite immune to uncorrelated measurement noise This paper also shows the theoretical relationship between the proposed methods and those of well-known resonant filters

[Modern spectral estimation of ICP-AES].

Abstract: The inductively coupled plasma atomic emission, spectrometry (ICP-AES) and its signal characteristics were discussed using modem spectral estimation technique The power spectra density (PSD) was calculated using the auto-regression (AR) model of modem spectra estimation The Levinson-Durbin recursion method was used to estimate the model parameters which were used for the PSD computation The results obtained with actual ICP-AES spectra and measurements showed that the spectral estimation technique was helpful for the better understanding about spectral composition and signal characteristics

Quasidistributions, tomography, and fractional Fourier transform in signal analysis

Abstract: The quasidistribution functions like the Ville-Wigner function, the Husimi-Kano function, and the coherent-state approach of Glauber and Sudarshan are reviewed in their application to signal analysis and information processing. Noncommutative tomography of an analytic signal and its relation to the fractional Fourier transform is discussed. The analogy of the analytic signal and the quantum wave function is used to show the identity of the fractional Fourier transform and the Green function of the harmonic oscillator. The approach is discussed for both time-dependent signals and spatial signals.

Spectral estimation of ARMA processes using ARMA-cepstrum recursion

Abstract: In this letter, the spectral estimation problem of a stationary autoregressive moving average (ARMA) process is considered, and a new method for the estimation of the MA part is proposed. A simple recursion relating the ARMA parameters and the cepstral coefficients of an ARMA process is derived and utilized for the estimation of the MA parameters. The method requires neither any initial estimates nor fitting of a large order AR model, both of which require further a priori knowledge of the signal and increase the computational complexity. Simulation results illustrating the performance of the new method are also given.

Low Order Equivalent System Identification for the Tu-144LL Supersonic Transport Aircraft

Abstract: Low order equivalent system models were identified from flight test data for the Tu-144LL supersonic transport aircraft. Flight test maneuvers were executed by Russian and American test pilots flying the aircraft from Zhukovsky airfield outside Moscow, Russia. Flight tests included longitudinal and lateral/directional maneuvers at supersonic cruise flight conditions. Piloted frequency sweeps and multi-step maneuvers were used to generate data for closed loop low order equivalent system modeling. Model parameters were estimated using a flexible, high accuracy Fourier transform and an equation error / output error (EE/OE) formulation in the frequency domain. Results were compared to parameter estimates obtained using spectral estimation and subsequent least squares fit to frequency response data in Bode plots. Modeling results from the two methods agreed well for both a frequency sweep and multiple concatenated multi-step maneuvers. For a single multi-step maneuver, the EE/OE method gave a better model fit with improved prediction capability. A summary of closed loop low order equivalent system identification results for the Tu-144LL, including estimated parameters, standard errors, and flying qualities level predictions, were computed and tabulated.

Detection of variable frequency signals using a fast chirp transform

Abstract: The detection of signals with varying frequency is important in many areas of physics and astrophysics. The current work was motivated by a desire to detect gravitational waves from the binary inspiral of neutron stars and black holes, a topic of significant interest for the new generation of interferometric gravitational wave detectors such as LIGO. However, this work has significant generality beyond gravitational wave signal detection. We define a fast chirp transform (FCT) analogous to the fast Fourier transform. Use of the FCT provides a simple and powerful formalism for detection of signals with variable frequency just as Fourier transform techniques provide a formalism for the detection of signals of constant frequency. In particular, use of the FCT can alleviate the requirement of generating complicated families of filter functions typically required in the conventional matched filtering process. We briefly discuss the application of the FCT to several signal detection problems of current interest.

Decimated Signal Diagonalization for Fourier Transform Spectroscopy

Abstract: A nonlinear parameter estimator with frequency-windowing for signal processing, called Decimated Signal Diagonalization (DSD), is presented. This method is used to analyze exponentially damped time signals of arbitrary length corresponding to spectra that are sums of pure Lorentzians. Such time signals typically arise in many experimental measurements, e.g., ion cyclotron resonance (ICR), nuclear magnetic resonance or Fourier transform infrared spectroscopy, etc. The results are compared with the standard spectral estimator, the Fast Fourier Transform (FFT). It is shown that the needed absorption spectra can be constructed simply, without any supplementary experimental work or concern about the phase problems that are known to plague FFT. Using a synthesized signal with known parameters, as well as experimentally measured ICR time signals, excellent results are obtained by DSD with significantly shorter acquisition time than that which is needed with FFT. Moreover, for the same signal length, DSD is demonstrated to exhibit a better resolving power than FFT.

The Accuracy of Time Series Analysis for Laser-Doppler Velocimetry

Abstract: Four approaches for the processing of unequally sampled data are known, each with many variants. The Lomb-Scargle approach uses the precise time information in computing spectra and is a useful method for the detection of harmonic peaks and much less for the spectral slope or other details. The second approach consists of several different slotting methods which determine an equidistant covariance estimate of the data. Unfortunately, none of the slotting covariance estimators has the important positive semi-definite property that is required for a valid covariance estimate. Hence, spectral estimates become negative at some frequencies and the logarithm of the spectrum is not defined there. Theoretically, no useful interpretation can be given to the estimates, because they no longer give the distribution of the total power over the frequencies. Many local peaks appear in the log spectral density between the negative spectral estimates if the negative estimated values are replaced by zero. The third category fits parametric spectral models to raw data. It imposes a spectral shape, independent of the data, and it can only be useful if that shape is known a priori. The fourth method first resamples the irregular data on an equidistant time base. Nearest Neighbor takes the nearest original observation for each resampled value. Afterwards, it uses the familiar and accurate equidistant signal processing algorithms for the evaluation. Time series models can give an accurate spectral representation for turbulence data, if the model type and the model order are selected properly. This is demonstrated by the fact that the spectral density is retrieved accurately with the spectrum of time series models in simulations. Resampling causes a distortion of the estimated spectrum, that increases strongly with frequency. Therefore, nearest neighbor resampling is limited in disclosing spectral details at higher frequencies. Although strongly filtered, peaks can be retrieved at frequencies up to the average sampling rate, so two times the Nyquist frequency that would belong to equidistant sampling. For still higher frequencies, even very strong peaks in the original irregular signal do not give rise to any ripple in the estimated spectral density after resampling.

Method and apparatus for modulation and demodulation related to orthogonal frequency division multiplexing

Abstract: Data pieces representative of in-phase components and quadrature components of a digital-modulation-resultant signal are assigned to frequencies for inverse fast Fourier transform. The inverse fast Fourier transform is executed at a predetermined sampling frequency Fs to convert the data pieces into a real-part signal and an imaginary-part signal. Phases of the real-part signal and the imaginary-part signal are shifted. Each of the phase-shifted real-part signal and the phase-shifted imaginary-part signal is divided into a sequence of even-numbered samples and a sequence of odd-numbered samples. A digital quadrature-modulation-resultant signal is generated from further manipulation of the even-numbered and odd-numbered samples.

Discussion on spatial resolution and sensitivity of Fourier transform fringe detection

Abstract: The spatial resolution and sensitivity of the Fourier transform method for fringe detection is analyzed. The spatial resolution degradation due to Fourier transform is discussed through a signal processing technique. It is found that the upper limit of spatial resolution for displacement measurement is half the carrier fringe pitch, or half the grid pitch for the grid method. The formulation of sensitivity using signal processing and communication theory is also performed and analyzed. Measures to improve the spatial resolution sensitivity are discussed.