Showing papers on "Spectral density estimation published in 2005"

Antileakage Fourier transform for seismic data regularization

Abstract: Seismic data regularization, which spatially transforms irregularly sampled acquired data to regularly sampled data, is a long-standing problem in seismic data processing. Data regularization can be implemented using Fourier theory by using a method that estimates the spatial frequency content on an irregularly sampled grid. The data can then be reconstructed on any desired grid. Difficulties arise from the nonorthogonality of the global Fourier basis functions on an irregular grid, which results in the problem of “spectral leakage”: energy from one Fourier coefficient leaks onto others. We investigate the nonorthogonality of the Fourier basis on an irregularly sampled grid and propose a technique called “antileakage Fourier transform” to overcome the spectral leakage. In the antileakage Fourier transform, we first solve for the most energetic Fourier coefficient, assuming that it causes the most severe leakage. To attenuate all aliases and the leakage of this component onto other Fourier coefficients, the data component corresponding to this most energetic Fourier coefficient is subtracted from the original input on the irregular grid. We then use this new input to solve for the next Fourier coefficient, repeating the procedure until all Fourier coefficients are estimated. This procedure is equivalent to “reorthogonalizing” the global Fourier basis on an irregularly sampled grid. We demonstrate the robustness and effectiveness of this technique with successful applications to both synthetic and real data examples.

Sampling and reconstruction of signals with finite rate of innovation in the presence of noise

Abstract: Recently, it was shown that it is possible to develop exact sampling schemes for a large class of parametric nonbandlimited signals, namely certain signals of finite rate of innovation. A common feature of such signals is that they have a finite number of degrees of freedom per unit of time and can be reconstructed from a finite number of uniform samples. In order to prove sampling theorems, Vetterli et al. considered the case of deterministic, noiseless signals and developed algebraic methods that lead to perfect reconstruction. However, when noise is present, many of those schemes can become ill-conditioned. In this paper, we revisit the problem of sampling and reconstruction of signals with finite rate of innovation and propose improved, more robust methods that have better numerical conditioning in the presence of noise and yield more accurate reconstruction. We analyze, in detail, a signal made up of a stream of Diracs and develop algorithmic tools that will be used as a basis in all constructions. While some of the techniques have been already encountered in the spectral estimation framework, we further explore preconditioning methods that lead to improved resolution performance in the case when the signal contains closely spaced components. For classes of periodic signals, such as piecewise polynomials and nonuniform splines, we propose novel algebraic approaches that solve the sampling problem in the Laplace domain, after appropriate windowing. Building on the results for periodic signals, we extend our analysis to finite-length signals and develop schemes based on a Gaussian kernel, which avoid the problem of ill-conditioning by proper weighting of the data matrix. Our methods use structured linear systems and robust algorithmic solutions, which we show through simulation results.

Quantifying errors in spectral estimates of HRV due to beat replacement and resampling

Abstract: Spectral estimates of heart rate variability (HRV) often involve the use of techniques such as the fast Fourier transform (FFT), which require an evenly sampled time series. HRV is calculated from the variations in the beat-to-beat (RR) interval timing of the cardiac cycle which are inherently irregularly spaced in time. In order to produce an evenly sampled time series prior to FFT-based spectral estimation, linear or cubic spline resampling is usually employed. In this paper, by using a realistic artificial RR interval generator, interpolation and resampling is shown to result in consistent over-estimations of the power spectral density (PSD) compared with the theoretical solution. The Lomb-Scargle (LS) periodogram, a more appropriate spectral estimation technique for unevenly sampled time series that uses only the original data, is shown to provide a superior PSD estimate. Ectopy removal or replacement is shown to be essential regardless of the spectral estimation technique. Resampling and phantom beat replacement is shown to decrease the accuracy of PSD estimation, even at low levels of ectopy or artefact. A linear relationship between the frequency of ectopy/artefact and the error (mean and variance) of the PSD estimate is demonstrated. Comparisons of PSD estimation techniques performed on real RR interval data during minimally active segments (sleep) demonstrate that the LS periodogram provides a less noisy spectral estimate of HRV.

Localized spectral analysis on the sphere

Abstract: It is often advantageous to investigate the relationship between two geophysical data sets in the spectral domain by calculating admittance and coherence functions. While there exist powerful Cartesian windowing techniques to estimate spatially localized (cross-)spectral properties, the inherent sphericity of planetary bodies sometimes necessitates an approach based in spherical coordinates. Direct localized spectral estimates on the sphere can be obtained by tapering, or multiplying the data by a suitable windowing function, and expanding the resultant field in spherical harmonics. The localization of a window in space and its spectral bandlimitation jointly determine the quality of the spatiospectral estimation. Two kinds of axisymmetric windows are here constructed that are ideally suited to this purpose: bandlimited functions that maximize their spatial energy within a cap of angular radius ?0, and spacelimited functions that maximize their spectral power within a spherical harmonic bandwidth L. Both concentration criteria yield an eigenvalue problem that is solved by an orthogonal family of data tapers, and the properties of these windows depend almost entirely upon the spacebandwidth product N0= (L+ 1) ?0/?. The first N0_1 windows are near perfectly concentrated, and the best-concentrated window approaches a lower bound imposed by a spherical uncertainty principle. In order to make robust localized estimates of the admittance and coherence spectra between two fields on the sphere, we propose a method analogous to Cartesian multitaper spectral analysis that uses our optimally concentrated data tapers. We show that the expectation of localized (cross-)power spectra calculated using our data tapers is nearly unbiased for stochastic processes when the input spectrum is white and when averages are made over all possible realizations of the random variables. In physical situations, only one realization of such a process will be available, but in this case, a weighted average of the spectra obtained using multiple data tapers well approximates the expected spectrum. While developed primarily to solve problems in planetary science, our method has applications in all areas of science that investigate spatiospectral relationships between data fields defined on a sphere.

/spl beta/-order MMSE spectral amplitude estimation for speech enhancement

Abstract: This paper proposes /spl beta/-order minimum mean-square error (MMSE) speech enhancement approach for estimating the short time spectral amplitude (STSA) of a speech signal. We analyze the characteristics of the /spl beta/-order STSA MMSE estimator and the relation between the value of /spl beta/ and the spectral amplitude gain function of the MMSE method. We further investigate the effectiveness of a range of fixed-/spl beta/ values in estimating STSA based on the MMSE criterion, and discuss how the /spl beta/ value could be adapted using the frame signal-to-noise ratio (SNR). The performance of the proposed speech enhancement approach is then evaluated through spectrogram inspection, objective speech distortion measures and subjective listening tests using several types of noise sources from the NOISEX-92 database. Evaluation results show that our approach can achieve a more significant noise reduction and a better spectral estimation of weak speech spectral components from a noisy signal as compared to many existing speech enhancement algorithms.

Noninvasive estimation of tissue temperature via high-resolution spectral analysis techniques

Abstract: We address the noninvasive temperature estimation from pulse-echo radio frequency signals from standard diagnostic ultrasound imaging equipment. In particular, we investigate the use of a high-resolution spectral estimation method for tracking frequency shifts at two or more harmonic frequencies associated with temperature change. The new approach, employing generalized second-order statistics, is shown to produce superior frequency shift estimates when compared to conventional high-resolution spectral estimation methods Seip and Ebbini (1995). Furthermore, temperature estimates from the new algorithm are compared with results from the more commonly used echo shift method described in Simon et al. (1998).

A generalized MVDR spectrum

Abstract: The minimum variance distortionless response (MVDR) approach is very popular in array processing. It is also employed in spectral estimation where the Fourier matrix is used in the optimization process. First, we give a general form of the MVDR where any unitary matrix can be used to estimate the spectrum. Second and most importantly, we show how the MVDR method can be used to estimate the magnitude squared coherence function, which is very useful in so many applications but so few methods exist to estimate it. Simulations show that our algorithm gives much more reliable results than the one based on the popular Welch's method.

Minimum variance distortionless response spectral estimation

Abstract: In this article, we concentrate on spectral estimation techniques that are useful in extracting the features to be used by automatic speech recognition (ASR) system. As an aid to understanding the spectral estimation process for speech signals, we adopt the source filter model of speech production as presented in X. Huang et al. (2001), wherein speech is divided into two broad classes: voiced and unvoiced. Voiced speech is quasi-periodic, consisting of a fundamental frequency corresponding to the pitch of a speaker, as well as its harmonics. Unvoiced speech is stochastic in nature and is best modeled as white noise convolved with an infinite impulse response filter.

On the resolvability of sinusoids with nearby frequencies in the presence of noise

Abstract: This correspondence develops statistical algorithms and performance limits for resolving sinusoids with nearby frequencies in the presence of noise. We address the problem of distinguishing whether the received signal is a single-frequency sinusoid or a double-frequency sinusoid, with possibly unequal, and unknown, amplitudes and phases. We derive a locally optimal detection strategy that can be applied in a standalone fashion or as a refinement step for existing spectral estimation methods to yield improved performance. We further derive explicit relationships between the minimum detectable difference between the frequencies of two tones for any particular false alarm and detection rate and at a given SNR.

Tutorial on Univariate Autoregressive Spectral Analysis

Abstract: In the present paper, the theoretical basis of autoregressive (AR) modelling in spectral analysis is explained in simple terms. Spectral analysis gives information about the frequency content and sources of variation in a time series. The AR method is an alternative to discrete Fourier transform, and the method of choice for high-resolution spectral estimation of a short time series. In biomedical engineering, AR modelling is used especially in the spectral analysis of heart rate variability and electroencephalogram tracings. In AR modelling, each value of a time series is regressed on its past values. The number of past values used is called the model order. An AR model or process may be used in either process synthesis or process analysis, each of which can be regarded as a filter. The AR analysis filter divides the time series into two additive components, the predictable time series and the prediction error sequence. When the prediction error sequence has been separated from the modelled time series, the AR model can be inverted, and the prediction error sequence can be regarded as an input and the measured time series as an output to the AR synthesis filter. When a time series passes through a filter, its amplitudes of frequencies are rescaled. The properties of the AR synthesis filter are used to determine the amplitude and frequency of the different components of a time series. Heart rate variability data are here used to illustrate the method of AR spectral analysis. Some basic definitions of discrete-time signals, necessary for understanding of the content of the paper, are also presented.

Application of the Random Decrement Technique in Operational Modal Analysis

Abstract: The random decrement (RD) technique is a time domain procedure, where the structural responses to operational loads are transformed into random decrement functions, which are proportional to the correlation functions of the system operational responses or can, equivalently, be considered as free vibration responses. This paper presents a general review on the application of the RD technique in operational modal analysis. It refers its application in association with time domain modal identification methods, like the Ibrahim time domain method or the stochastic subspace covariance driven method. It also describes the use of the RD technique in association with frequency domain output-only modal identification methods, like the frequency domain decomposition method (FDD). A practical example is given showing the results obtained from ambient vibration tests performed in a civil engineering structure.

Multispectral synthesis of daylight using a commercial digital CCD camera.

Abstract: Performance of multispectral devices in recovering spectral data has been intensively investigated in some applications, as in spectral characterization of art paintings, but has received little attention in the context of spectral characterization of natural illumination. This study investigated the quality of the spectral estimation of daylight-type illuminants using a commercial digital CCD camera and a set of broadband colored filters. Several recovery algorithms that did not need information about spectral sensitivities of the camera sensors nor eigenvectors to describe the spectra were tested. Tests were carried out both with virtual data, using simulated camera responses, and real data obtained from real measurements. It was found that it is possible to recover daylight spectra with high spectral and colorimetric accuracy with a reduced number of three to nine spectral bands.

Parametric speech codec for representing synthetic speech in the presence of background noise

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.

Adaptive modeling and spectral estimation of nonstationary biomedical signals based on Kalman filtering

Abstract: We describe an algorithm to estimate the instantaneous power spectral density (PSD) of nonstationary signals. The algorithm is based on a dual Kalman filter that adaptively generates an estimate of the autoregressive model parameters at each time instant. The algorithm exhibits superior PSD tracking performance in nonstationary signals than classical nonparametric methodologies, and does not assume local stationarity of the data. Furthermore, it provides better time-frequency resolution, and is robust to model mismatches. We demonstrate its usefulness by a sample application involving PSD estimation of intracranial pressure signals (ICP) from patients with traumatic brain injury (TBI).

Rhythm Classification using spectral rhythm patterns

Abstract: In this paper, we study the use of spectral patterns to represent the characteristics of the rhythm of an audio signal. A function representing the position of onsets over time is first extracted from the audio signal. From this function we compute at each time a vector which represents the characteristics of the local rhythm. Three feature sets are studied for this vector. They are derived from the amplitude of the Discrete Fourier Transform, the AutoCorrelation Function and the product of the DFT and of a Frequency-Mapped ACF. The vectors are then sampled at some specific frequencies, which represents various ratios of the local tempo. The ability of the three feature sets to represent the rhythm characteristics of an audio item is evaluated through a classification task. We show that using such simple spectral representations allows obtaining results comparable to the state of the art.

Dimensional Normalization in the Digital Computation of the Fractional Fourier Transform

Abstract: The fast algorithm of the digital computation of the fractional Fourier transform(FRFT) requires the dimensional normalization, but how to do it for practical discrete signal is not settled yet For this reason, the paper presents two engineering-oriented methods of the dimensional normalization One is called as the discrete scaling transform method, another is called as the data zero-padding/interception method Furthermore, their effects on the parameter estimation of the chirp signal are studied and for discrete scaling method, a relationship before and after the normalization is developed Finally, these methods are verified by simulation examples These engineering-oriented methods of the dimensional normalization makes the FRFT more practical in digital signal processing

Channel estimation for a communication system using spectral estimation

Abstract: Techniques for performing channel estimation in a multi-carrier system are described A frequency response estimate is initially obtained for a wireless channel based on a narrowband pilot sent on different sets of subbands in different symbol periods or a wideband pilot sent on all or most subbands in the system Spectral estimation is performed on the frequency response estimate to determine at least one frequency component of the frequency channel estimate, with each frequency component being indicative of a delay for a channel tap in an impulse response estimate for the wireless channel A channel estimate for the wireless channel is then obtained based on the frequency component(s) determined by the spectral estimation This channel estimate may be a channel profile, the impulse response estimate, an improved frequency response estimate, a signal arrival time, or some other pertinent information regarding the wireless channel

Accurate and robust frequency estimation in the ODFT domain

Abstract: This paper presents new results improving by a factor of 10 the accuracy of an odd-DFT based frequency estimation algorithm. These results are shown to be robust to the influence of additive noise and compare favorably to other non-iterative frequency domain estimation algorithms. A perspective is given on possible application areas, namely those involving real-time constraints

Rank-deficient robust Capon filter bank approach to complex spectral estimation

Abstract: We consider nonparametric complex spectral estimation using an adaptive filtering-based approach where the finite-impulse response (FIR) filter bank is obtained via a rank-deficient robust Capon beamformer. We show that, by allowing the sample covariance matrix to be rank deficient, we can achieve much higher resolution than existing approaches, which is useful in many applications, including radar target detection and feature extraction. Numerical examples are provided to demonstrate the performance of the new approach as compared to the existing data-adaptive and data-independent FIR filtering-based spectral estimation methods.

Frequency responses and resolving power of numerical integration of sampled data.

Abstract: Methods of numerical integration of sampled data are compared in terms of their frequency responses and resolving power. Compared, theoretically and by numerical experiments, are trapezoidal, Simpson, Simpson-3/8 methods, method based on cubic spline data interpolation and Discrete Fourier Transform (DFT) based method. Boundary effects associated with DFT- based and spline-based methods are investigated and an improved Discrete Cosine Transform based method is suggested and shown to be superior to all other methods both in terms of approximation to the ideal continuous integrator and of the level of the boundary effects.

Fractional Fourier transform for sonar signal processing

Abstract: In this paper we present an approach for processing of sonar signals with the ultimate goal of ocean bottom sediment classification. Work reported is based on sonar data collected by the volume search sonar (VSS) in the Gulf of Mexico, as well as on VSS synthetic data. The volume search sonar is a beam formed multibeam sonar system with 27 fore and 27 aft beams, covering almost the entire water volume (from above horizontal, through vertical, back to above horizontal). Our investigation is focused on the bottom-return signals since we are interested in determination of the impulse response of the ocean bottom floor. The bottom-return signal is the convolution between the impulse response of the bottom floor and the transmitted sonar chirp signal. The method developed here is based on fractional Fourier transform, a fundamental tool for signal processing and optical information processing. Fractional Fourier transform is a generalization of the classical Fourier transform. The traditional Fourier transform decomposes signal by sinusoids whereas Fractional Fourier transform corresponds to expressing the signal in terms of an orthonormal basis formed by chirps. In recent years, interest in and use of time-frequency tools have increased and become more suitable for sonar applications. The fractional Fourier transform requires finding the optimum order of the transform that can be estimated based on the properties of the chirp signal. The bottom impulse response is given by the magnitude of the fractional Fourier transform applied to the bottom return signal. The technique used in this work has been tested both on synthetic data and real sonar data collected by the VSS. The synthetic sonar return signal has been generated by the convolution between the Green function, which has been utilized to simulate the impulse response of the seafloor and the transmitted VSS chirp. A study is carried out to compare the performance of our method to a conventional method based on deconvolution in the frequency domain (using standard Fourier transform). The amplitude and shape of an acoustic signal reflected from the sea floor is determined mainly by the seabottom roughness, the density difference between water and the sea floor, and reverberation within the substrate. Since the distribution of seafloor types is a very important tool in different applications, a sediment classification has been implemented based on a statistical analysis of the obtained impulse response. In order to perform a robust analysis of the signal, a joint time-frequency analysis is necessary. In this paper the analysis has been evaluated using the Wigner distribution, which can be thought of as a signal energy distribution in joint time-frequency domain. Singular value decomposition of the Wigner distribution has been used in order to perform the seafloor sediment classification. A comparative analysis of the experimental results for classical deconvolution and fractional Fourier method is presented. Results are shown and suggestions for future work are provided

Audio signal decoding using complex-valued data

Abstract: A decoder particularly, but not exclusively, for MPEG-1 layer III data signals, in which recovered spectral coefficients are transformed into time domain signal components, the time domain signal components then being transformed, using a forward transform which is orthogonally modulated with respect to the forward transform that was used at the encoder, to produce a set of second spectral coefficients. In this way, the first and second spectral coefficients may be used as complex-valued spectral coefficients which are amenable to post­-processing. In the preferred embodiment, the complex-valued frequency components are, after post-processing, transformed to the time domain using an odd-frequency modulated Discrete Fourier Transform (DFT).

State-space spectral estimation of characteristic electromagnetic responses in wideband data

Abstract: This letter utilizes a robust spectral estimation method, based on state-space control theory, to coherently process wideband frequency domain field data of any object and extract specific modal (or characteristic) responses associated with wave propagation along the object. The estimation problem is formulated in terms of well-known range processing used in radar imaging. Thus, the data is modeled in terms of complex sinusoids, whose amplitude is scaled by the decay constants of the modes and whose phase yields the range associated with scattering centers pertinent to modal propagation. Unlike other approaches that require the system poles to be inside the unit circle, the complex poles yielding the decay constants in the proposed approach can be located anywhere in the z-plane, and can vary with frequency, in order to capture the dynamic wideband behavior of the scattering mechanism. The method is illustrated by application to mode extraction for a cylindrically stratified dielectric scatterer.

Estimation of 2-D ARMA model parameters by using equivalent AR approach

Abstract: In this paper, the problem of estimating the parameters of a two-dimensional autoregressive moving-average (2-D ARMA) model driven by an unobservable input noise is addressed. In order to solve this problem, the relation between the parameters of a 2-D ARMA model and their 2-D equivalent autoregressive (EAR) model parameters is investigated. Based on this relation, a new algorithm is proposed for determining the 2-D ARMA model parameters from the coefficients of the 2-D EAR model. This algorithm is a three-step approach. In the first step, the parameters of the 2-D EAR model that is approximately equivalent to the 2-D ARMA model are estimated by applying 2-D modified Yule–Walker (MYW) equation to the process under consideration. Then, the moving-average parameters of the 2-D ARMA model are obtained solving the linear equation set constituted by using the EAR coefficients acquired in the first step. Finally, the autoregressive parameters of the 2-D ARMA model are found by exploiting the values obtained in first and second steps. The performance of the proposed algorithm is compared with other 2-D ARMA parameter and spectral estimation algorithms available in the technical literature by means of three different criteria. As a result of this comparison, it is shown that the parameters and the corresponding power spectrums estimated by using the proposed algorithm are converged to the original parameters and the original power spectrums, respectively.

The fast Fourier transform for experimentalists. Part III. Classical spectral analysis

Abstract: Each article in this continuing series on the fast Fourier transform (FFT) is designed to illuminate new features of the wide-ranging applicability of this transform. This segment deals with some aspects of the spectrum estimation problem.

Hilbert-Huang Transform and Its Application in Gear Faults Diagnosis

Abstract: Time-frequency and transient analysis have been widely used in signal processing and faults diagnosis. These methods represent important characteristics of a signal in both time and frequency domain. In this way, essential features of the signal can be viewed and analyzed in order to understand or model the faults characteristics. Historically, Fourier spectral analyses have provided a general approach for monitoring the global energy/frequency distribution. However, an assumption inherent to this method is the stationary and linear of the signal. As a result, Fourier methods are not generally an appropriate approach in the investigation of faults signals with transient components. This work presents the application of a new signal processing technique, empirical mode decomposition and the Hilbert spectrum, in analysis of vibration signals and gear faults diagnosis for a machine tool. The results show that this method may provide not only an increase in the spectral resolution but also reliability for the gear faults diagnosis.