Showing papers on "Spectral density estimation published in 2010"
TL;DR: A variant of Synchrosqueezing is considered, based on the short-time Fourier transform, to precisely define the instantaneous frequencies of a multicomponent AM-FM signal and an algorithm to recover these instantaneous frequencies from the uniform or nonuniform samples of the signal is described.
Abstract: We propose a new approach for studying the notion of the instantaneous frequency of a signal. We build on ideas from the Synchrosqueezing theory of Daubechies, Lu and Wu and consider a variant of Synchrosqueezing, based on the short-time Fourier transform, to precisely define the instantaneous frequencies of a multi-component AM-FM signal. We describe an algorithm to recover these instantaneous frequencies from the uniform or nonuniform samples of the signal and show that our method is robust to noise. We also consider an alternative approach based on the conventional, Hilbert transform-based notion of instantaneous frequency to compare to our new method. We use these methods on several test cases and apply our results to a signal analysis problem in electrocardiography.
240 citations
TL;DR: In this paper, the authors consider nonparametric estimation of spectral densities of stationary processes, and obtain consistency and asymptotic normality of spectral density estimates under natural and easily verifiable conditions.
Abstract: We consider nonparametric estimation of spectral densities of stationary processes, a fundamental problem in spectral analysis of time series. Under natural and easily verifiable conditions, we obtain consistency and asymptotic normality of spectral density estimates. Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. The latter result sheds new light on the classical problem of tests of white noises.
99 citations
TL;DR: This work presents the application of high resolution 5D experiments for protein backbone assignment and measurements of coupling constants from the 4D E.COSY multiplets to demonstrate how Discrete Fourier transform opens an avenue to NMR techniques of ultra-high resolution and dimensionality.
74 citations
TL;DR: The analysis of a periodic signal with localized random noise is given by using harmonic wavelets by defining a projection wavelet operator the signal is automatically decomposed into the localized pulse and the periodic function.
Abstract: The analysis of a periodic signal with localized random (or high frequency) noise is given by using harmonic wavelets. Since they are orthogonal to the Fourier basis, by defining a projection wavelet operator the signal is automatically decomposed into the localized pulse and the periodic function. An application to the analysis of a self-similar non-stationary noise is also given.
72 citations
TL;DR: In this paper, the problem of estimating the fractional order of a Levy process from low frequency historical and options data is considered and an estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way.
Abstract: We consider the problem of estimating the fractional order of a Levy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. The corresponding procedure consists of two steps: the estimation of a conditional characteristic function and the weighted least squares estimation of the fractional order in spectral domain. While the second step is identical for both calibration and estimation, the first one depends on the problem at hand. Minimax rates of convergence for the fractional order estimate are derived, the asymptotic normality is proved and a data-driven algorithm based on aggregation is proposed. The performance of the estimator in both estimation and calibration setups is illustrated by a simulation study.
67 citations
TL;DR: The results show that the dynamic range as well as the resolution of the ISAR images plays an important role in the identiflcation performance, and the optimum size of the subarray for MUSIC and MEMP-MUSIC in terms of target identIFlcation is experimentally derived.
Abstract: Inverse synthetic aperture radar (ISAR) images represent the two-dimensional (2-D) spatial distribution of the radar cross- section (RCS) of an object and, thus, they can be applied to the problem of target identiflcation. The traditional approach to ISAR imaging is the range-Doppler algorithm based on the 2-D Fourier transform. However, the 2-D Fourier transform often results in poor resolution ISAR images, especially when the measured frequency bandwidth and angular region are limited. Instead of the Fourier transform, high resolution spectral estimation techniques can be adopted to improve the resolution of ISAR images. These are the autoregressive (AR) model, multiple signal classiflcation (MUSIC), and matrix enhancement and matrix pencil MUSIC (MEMP-MUSIC). In this study, the ISAR images from these high-resolution spectral estimators, as well as the FFT approach, are identifled using a recently developed identiflcation algorithm based on the polar mapping of ISAR images. In addition, each ISAR imaging algorithm is analyzed and compared in the framework of radar target identiflcation. The results show that the dynamic range as well as the resolution of the ISAR images plays an important role in the identiflcation performance. Moreover, the optimum size of the subarray (i.e., covariance matrix) for MUSIC and MEMP-MUSIC in terms of target identiflcation is experimentally derived.
62 citations
TL;DR: A new approach based on eigen-systems pseudo-spectral estimation methods, namely Eigenvector and MUSIC , and Multiple Layer Perceptron (MLP) neural network is introduced that can make the practical and real-time detection of this chronic disease feasible.
60 citations
TL;DR: A one-dimensional power spectral density analysis of the fabric image via a Burg-algorithm-based Auto-Regressive (AR) spectral estimation model, and accordingly extracts features capable of effectively differentiating normal textures from defective ones.
Abstract: For the purpose of realizing fast and effective detection of defects in woven fabric, and in consideration of the inherent characteristics of fabric texture, i.e., periodicity and orientation, a new approach for fabric texture analysis, based on the modern spectral analysis of a time series rather than the classical spectral analysis of an image, is proposed in this paper. Traditionally, a power spectral estimated by a two-dimensional Fast Fourier transformation (FFT) is usually employed in the detection of fabric defects, which involves a large computational complexity and a relatively low accuracy of spectral estimation. To this effect, this paper makes a one-dimensional power spectral density (PSD) analysis of the fabric image via a Burg-algorithm-based Auto-Regressive (AR) spectral estimation model, and accordingly extracts features capable of effectively differentiating normal textures from defective ones. A support vector data description is adopted as a detector in order to deal with defect detecti...
46 citations
TL;DR: In this paper, an effective and simple way to reconstruct displacement signal from a measured acceleration signal is proposed, which utilizes curve-fitting around the significant frequency components of the Fourier transform of the acceleration signal before it is inverse-Fourier transformed.
Abstract: An effective and simple way to reconstruct displacement signal from a measured acceleration signal is proposed in this paper. To reconstruct displacement signal by means of double-integrating the time domain acceleration signal, the Nyquist frequency of the digital sampling of the acceleration signal should be much higher than the highest frequency component of the signal. On the other hand, to reconstruct displacement signal by taking the inverse Fourier transform, the magnitude of the significant frequency components of the Fourier transform of the acceleration signal should be greater than the 6 dB increment line along the frequency axis. With a predetermined resolution in time and frequency domain, determined by the sampling rate to measure and record the original signal, reconstructing high-frequency signals in the time domain and reconstructing low-frequency signals in the frequency domain will produce biased errors. Furthermore, because of the DC components inevitably included in the sampling process, low-frequency components of the signals are overestimated when displacement signals are reconstructed from the Fourier transform of the acceleration signal. The proposed method utilizes curve-fitting around the significant frequency components of the Fourier transform of the acceleration signal before it is inverse-Fourier transformed. Curve-fitting around the dominant frequency components provides much better results than simply ignoring the insignificant frequency components of the signal.
45 citations
TL;DR: In this paper, the authors consider the statistical experiment given by a sample y(1 ),..., y(n) of a stationary Gaussian process with an unknown smooth spectral density f.
Abstract: We consider the statistical experiment given by a sample y(1 ), ... , y(n) of a stationary Gaussian process with an unknown smooth spectral density f . Asymptotic equivalence, in the sense of Le Cam's deficiency Δ-distance, to two Gaussian experiments with simpler structure is established. The first one is given by independent zero mean Gaussians with variance approximately f (ω i ), where ω i is a uniform grid of points in (-π, π) (nonparametric Gaussian scale regression). This approximation is closely related to well-known asymptotic independence results for the periodogram and corresponding inference methods. The second asymptotic equivalence is to a Gaussian white noise model where the drift function is the log-spectral density. This represents the step from a Gaussian scale model to a location model, and also has a counterpart in established inference methods, that is, log-periodogram regression. The problem of simple explicit equivalence maps (Markov kernels), allowing to directly carry over inference, appears in this context but is not solved here.
43 citations
03 May 2010
TL;DR: This paper proposes a fast interpolation method, independent of the window type and order, based on suitable lookup tables, proving that the method provides results as good as those obtained with other methods, without requiring the same high computation burden.
Abstract: The evaluation of the spectral components of a signal by means of discrete Fourier transform or fast Fourier transform algorithms is subject to leakage errors whenever the sampling frequency is not coherent with the signal frequency. Smoothing windows are used to mitigate these errors, and interpolation methods are applied in the frequency domain to reduce them further on. However, if cosine windows are employed, closed-form formulas for the evaluation of harmonic frequencies can be used only with the Rife-Vincent class I windows, while approximated formulas have to be used in other cases. In both cases, a high computation burden is required. This paper proposes a fast interpolation method, independent of the window type and order, based on suitable lookup tables. Experimental results are reported, and the accuracy is discussed, proving that the method provides results as good as those obtained with other methods, without requiring the same high computation burden.
TL;DR: A new time-varying autoregressive (TVAR) modelling approach is proposed for non-stationary signal processing and analysis, with application to EEG data modelling and power spectral estimation using a novel multiwavelet decomposition scheme.
Abstract: A new time-varying autoregressive (TVAR) modelling approach is proposed for non-stationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multiwavelet decomposition scheme. The time-varying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method.
TL;DR: In this article, the authors extend the classical spectral estimation problem to the infinite-dimensional case and propose a new approach to this problem using the Boundary Control (BC) method.
Abstract: We extend the classical spectral estimation problem to the
infinite-dimensional case and propose a new approach to this
problem using the Boundary Control (BC) method. Several
applications to inverse problems for partial differential
equations are provided.
TL;DR: Comparison of spectral estimation methods showed that the Welch method provided spectra yielding more accurate and precise backscatter coefficient and scatterer size estimations than spectra computed by applying rectangular, Hanning, or Hamming windows and much reduced computational load than if using the multitaper method.
Abstract: By analyzing backscattered echo signal power spectra and thereby obtaining backscatter coefficient vs frequency data, the size of subresolution scatterers contributing to echo signals can be estimated Here we investigate trade-offs in data acquisition and processing parameters for reference phantom-based backscatter and scatterer size estimations RF echo data from a tissue-mimicking test phantom were acquired using a clinical scanner equipped with linear array transducers One array has a nominal frequency bandwidth of 5 to 13 MHz and the other 4 to 9 MHz Comparison of spectral estimation methods showed that the Welch method provided spectra yielding more accurate and precise backscatter coefficient and scatterer size estimations than spectra computed by applying rectangular, Hanning, or Hamming windows and much reduced computational load than if using the multitaper method For small echo signal data block sizes, moderate improvements in scatterer size estimations were obtained using a multitaper method, but this significantly increases the computational burden It is critical to average power spectra from lateral A-lines for the improvement of scatterer size estimation Averaging approximately 10 independent A-lines laterally with an axial window length 10 times the center frequency wavelength optimized trade-offs between spatial resolution and the variance of scatterer size estimates Applying the concept of a time-bandwidth product, this suggests using analysis blocks that contain at least 30 independent samples of the echo signal The estimation accuracy and precision depend on the ka range where k is the wave number and a is the effective scatterer size This introduces a region-of-interest depth dependency to the accuracy and precision because of preferential attenuation of higher frequency sound waves in tissue-like media With the 5 to 13 MHz, transducer ka ranged from 05 to 16 for scatterers in the test phantom, which is a favorable range, and the accuracy and precision of scatterer size estimations were both within ~5% using optimal analysis block dimensions When the 4- to 9-MHz transducer was used, the ka value ranged from 03 to 08 to 11 for the experimental conditions, and the accuracy and precision were found to be ~10% and 10% to 25%, respectively Although the experiments were done with 2 specific models of transducers on the test phantom, the results can be generalized to similar clinical arrays available from a variety of manufacturers and/or for different size of scatterers with similar ka range
TL;DR: This paper addresses the reconstruction of compactly supported functions from non-uniform samples of their Fourier transform with convolutional gridding and uniform re-sampling, and investigates the reconstruction accuracy as it relates to sampling density.
Abstract: This paper addresses the reconstruction of compactly supported functions from non-uniform samples of their Fourier transform. We briefly investigate the consequences of acquiring non-uniform spectral data. We summarize two often applied reconstruction methods, convolutional gridding and uniform re-sampling, and investigate the reconstruction accuracy as it relates to sampling density. Finally, we provide preliminary results from employing spectral re-projection methods in the reconstruction.
TL;DR: A new nonparametric iterative adaptive approach that provides a solution to the problem of estimating the spectral content of exponentially decaying signals from a set of irregularly sampled data and the damping coefficient, or linewidth, is explicitly modeled, which allows for an improved estimation performance.
TL;DR: Fast, stable, nonrecursive formulae are derived, based on time shifting properties of the pertinent variables, for spectral analysis of time varying signals, and efficient frequency domain recursive least squares based algorithms for the adaptive estimation of the power spectra are developed.
Abstract: In this paper fast algorithms for adaptive Capon and amplitude and phase estimation (APES) methods for spectral analysis of time varying signals, are derived. Fast, stable, nonrecursive formulae are derived, based on time shifting properties of the pertinent variables. As a consequence, efficient frequency domain recursive least squares (RLS) based, as well as fast RLS based algorithms for the adaptive estimation of the power spectra are developed. Stability issues of the frequency domain estimators are considered, and stabilization procedures are proposed. The computational complexity of the proposed algorithms is lower than relevant existing methods. The performance of the proposed algorithms is demonstrated through extensive simulations.
TL;DR: A novel method for the identification of characteristic components in frequency domain based on singularity analysis is proposed, in which Lipschitz exponent function is constructed from the signal through wavelet-based singularityAnalysis.
Abstract: In rotating machinery condition monitoring, identification of characteristic components is fundamental in many engineering applications so as to obtain fault sensitive features for fault detection and diagnosis. This paper proposed a novel method for the identification of characteristic components in frequency domain based on singularity analysis. In this process, Lipschitz exponent function is constructed from the signal through wavelet-based singularity analysis. In order to highlight the periodic phenomena, autocorrelation transform is employed to extract the periodic exponents and Fourier transform is used to map the time-domain information into frequency domain. Case study with rolling element bearing vibration data shows that the proposed has very excellent capability for the identification of characteristic components compared with traditional methods.
TL;DR: A comparison of computation time taken for spectrum estimation analysis is presented in this paper and the method which takes the shortest time for analysis is selected for real time application purpose.
Abstract: Dominant frequency (DF) of electrophysiological data is an effective approach to estimate the activation rate during Atrial Fibrillation (AF) and it is important to understand the pathophysiology of AF and to help select candidate sites for ablation. Frequency analysis is used to find and track DF. It is important to minimize the catheter insertion time in the atria as it contributes to the risk for the patients during this procedure, so DF estimation needs to be obtained as quickly as possible. A comparison of computation tim- es taken for spectrum estimation analysis is presented in this paper. Fast Fourier Transform (FFT), Blackman-Tukey (BT), Autoregressive (AR) and Multiple Signal Classification (MUSIC) methods are used to obtain the frequency spectrum of the signals. The time to produce DF was measured for each method. The method which takes the shortest time for analysis is selected for real time application purpose.
TL;DR: Results indicate that the spectral content of OCT signals can be used to estimate scatterer size and to classify dissimilar areas in phantoms and tissues with sensitivity and specificity of more than 90%.
Abstract: A novel spectral analysis technique of OCT images is demonstrated in this paper for classification and scatterer size estimation. It is based on SOCT autoregressive spectral estimation techniques and statistical analysis. Two different statistical analysis methods were applied to OCT images acquired from tissue phantoms, the first method required prior information on the sample for variance analysis of the spectral content. The second method used k-means clustering without prior information for the sample. The results are very encouraging and indicate that the spectral content of OCT signals can be used to estimate scatterer size and to classify dissimilar areas in phantoms and tissues with sensitivity and specificity of more than 90%.
14 Mar 2010
TL;DR: A noise level estimator using minimal values of the Short Time Fourier Transform of a signal embedded in a white Gaussian noise to estimate the variance of the noise without any a priori knowledge on the signal.
Abstract: In this paper we present a noise level estimator using minimal values of the Short Time Fourier Transform of a signal embedded in a white Gaussian noise. The spectral kurtosis of the smallest values is used to estimate the variance of the noise without any a priori knowledge on the signal. This estimation is illustrated on both a synthetic and speech signal. A dolphin whistle detection in underwater noise is given as an application.
TL;DR: A frequency domain SNR estimator in mobile communications is put forward, where the signal model with the band-limited fading channel and the additive white Gaussian noise is exploited and the noise power spectrum density can be estimated from the periodogram of channel-plus-noise signals, subsequently leading to SNR estimation.
TL;DR: The concept of adaptive decomposition of signals into basic building blocks, of which each of the non-negative analytic instantaneous frequency are called mono-components, is introduced and the terminology mono-component used in signal analysis is justified.
Abstract: We introduce the concept of adaptive decomposition of signals into basic building blocks, of which each of the non-negative analytic instantaneous frequency are called mono-components. We propose certain methods based on p-starlike functions and Fourier expansions for such decomposition. We justify the terminology mono-component used in signal analysis.
TL;DR: In this article, the problem of estimating the fractional order of a Levy process from low frequency historical and options data is considered and an estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way.
Abstract: We consider the problem of estimating the fractional order of a Levy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. The corresponding procedure consists of two steps: the estimation of a conditional characteristic function and the weighted least squares estimation of the fractional order in spectral domain. While the second step is identical for both calibration and estimation, the first one depends on the problem at hand. Minimax rates of convergence for the fractional order estimate are derived, the asymptotic normality is proved and a data-driven algorithm based on aggregation is proposed. The performance of the estimator in both estimation and calibration setups is illustrated by a simulation study.
14 Mar 2010
TL;DR: A Bayesian based iterative algorithm is described that discovers the set of active signals conforming the band and simultaneously reconstructs the spectrum and is shown to perform close to a Genie-Aided CRLB that includes full knowledge about the sparsity pattern of the channels.
Abstract: In Cognitive Radio scenarios channelization information from primary network may be available to the spectral monitor. Under this assumption we propose a spectral estimation algorithm from compressed measurements of a multichannel wideband signal. The analysis of the Cramer-Rao Lower Bound (CRLB) for this estimation problem shows the importance of detecting the underlaying sparsity pattern of the signal. To this end we describe a Bayesian based iterative algorithm that discovers the set of active signals conforming the band and simultaneously reconstructs the spectrum. This iterative spectral estimator is shown to perform close to a Genie-Aided CRLB that includes full knowledge about the sparsity pattern of the channels.
Patent•
03 May 2010TL;DR: In this paper, the authors proposed a method for estimating the fundamental frequency of a speech signal based on the cross-correlation function of the signal spectrum of the speech signal and the time domain.
Abstract: The invention provides a method for estimating a fundamental frequency of a speech signal comprising the steps of receiving a signal spectrum of the speech signal, filtering the signal spectrum to obtain a refined signal spectrum, determining a cross-power spectral density using the refined signal spectrum and the signal spectrum, transforming the cross-power spectral density into the time domain to obtain a cross-correlation function, and estimating the fundamental frequency of the speech signal based on the cross-correlation function.
TL;DR: In this article, a postprocessing method based on the high-resolution spectral estimation via the Yule-Walker method is proposed to overcome the difficulty of estimating the energy bands of a phononic crystal.
Abstract: If the energy bands of a phononic crystal are calculated by the finite difference time domain (FDTD) method combined with the fast Fourier transform (FFT), good estimation of the eigenfrequencies can only be ensured by the postprocessing of sufficiently long time series generated by a large number of FDTD iterations. In this paper, a postprocessing method based on the high-resolution spectral estimation via the Yule–Walker method is proposed to overcome this difficulty. Numerical simulation results for three-dimensional acoustic and two-dimensional elastic systems show that, compared with the classic FFT-based postprocessing method, the proposed method can give much better estimation of the eigenfrequencies when the FDTD is run with relatively few iterations.
29 Sep 2010
TL;DR: In this paper, a matched filter is implemented for a chirp radar signal in the optimum fractional Fourier transform (FrFT) domain using the principle of stationary phase (PSP).
Abstract: -A matched filter is the optimal linear filter for maximizing the signal to noise ratio (SNR) in the presence of additive noise. Matched filters are commonly used in radar systems where the transmitted signal is known and may be used as a replica to be correlated with the received signal which can be carried out by multiplication in the frequency domain by applying Fourier Transform (FT). Fractional Fourier transform (FrFT) is the general case for the FT and is superior in chirp pulse compression using the optimum FrFT order. In this paper a matched filter is implemented for a chirp radar signal in the optimum FrFT domain. Mathematical formula for a received chirp signal in the frequency domain and a generalized formula in the fractional Fourier domain are presented in this paper using the Principle of Stationary Phase (PSP). These mathematical expressions are used to show the limitations of the matched filter in the fractional Fourier domain. The parameters that affect the chirp signal in the optimum fractional Fourier domain are described. The performance enhancement by using the matched filter in the fractional Fourier domain for special cases is presented.
20 Jun 2010
TL;DR: An AR signal-processing model for the epileptic EEG is proposed, which results in a reduction of analysis time by the expert neurologist, and can be implemented in real-time on a small microcomputer system for on-line analysis.
Abstract: Epilepsy is a chronic neurological disorder characterized by recurrent, unprovoked seizures. This study deals with a preliminary investigation to detect epileptic components in the electroencephalogram (EEG) waveform, which results in a reduction of analysis time by the expert neurologist. As an alternative to the Fast Fourier Transform (FFT) spectral analysis approach, an Auto Regressive (AR), a Moving Average (MA) and an Auto Regressive Moving Average (ARMA) model-based spectral estimators can be used to process the EEG signal. An AR signal-processing model for the epileptic EEG is proposed. The AR modelling has been used to analyse physiological signals such as the human EEG. The interpretation of an autoregressive model as a recursive digital filter and its use in spectral estimation are considered. This is used to formulate an analysis model, based on Linear Prediction Coding (LPC). The theory behind the method is explained and the implementation is described. The algorithm is computationally efficient and can be implemented in real-time on a small microcomputer system for on-line analysis. Results produced by this method may be used for further analysis.
TL;DR: In this article, the performance of high-resolution quadratic time-frequency distributions (TFDs) including the ones obtained by the reassignment method, the optimal radially Gaussian kernel method, and the t-f autoregressive moving-average spectral estimation method and the neural network-based method were rigorously compared to each other using several objective measures.
Abstract: This work evaluates the performance of high-resolution quadratic time-frequency distributions (TFDs) including the ones obtained by the reassignment method, the optimal radially Gaussian kernel method, the t-f autoregressive moving-average spectral estimation method and the neural network-based method. The approaches are rigorously compared to each other using several objective measures. Experimental results show that the neural network-based TFDs are better in concentration and resolution performance based on various examples.