Showing papers on "Spectral density estimation published in 2013"
TL;DR: This paper extends to signals on graphs DSP and its basic tenets, including filters, convolution, z-transform, impulse response, spectral representation, Fourier transform, frequency response, and illustrates DSP on graphs by classifying blogs, linear predicting and compressing data from irregularly located weather stations, or predicting behavior of customers of a mobile service provider.
Abstract: In social settings, individuals interact through webs of relationships. Each individual is a node in a complex network (or graph) of interdependencies and generates data, lots of data. We label the data by its source, or formally stated, we index the data by the nodes of the graph. The resulting signals (data indexed by the nodes) are far removed from time or image signals indexed by well ordered time samples or pixels. DSP, discrete signal processing, provides a comprehensive, elegant, and efficient methodology to describe, represent, transform, analyze, process, or synthesize these well ordered time or image signals. This paper extends to signals on graphs DSP and its basic tenets, including filters, convolution, z-transform, impulse response, spectral representation, Fourier transform, frequency response, and illustrates DSP on graphs by classifying blogs, linear predicting and compressing data from irregularly located weather stations, or predicting behavior of customers of a mobile service provider.
1,432 citations
TL;DR: It is demonstrated that the SDP outperforms the l1 optimization which outperforms MUSIC, Cadzow's, and Matrix Pencil approaches in terms of MSE over a wide range of signal-to-noise ratios.
Abstract: Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without knowledge of the model order. We propose an abstract theory of denoising with atomic norms and specialize this theory to provide a convex optimization problem for estimating the frequencies and phases of a mixture of complex exponentials. We show that the associated convex optimization problem can be solved in polynomial time via semidefinite programming (SDP). We also show that the SDP can be approximated by an l1-regularized least-squares problem that achieves nearly the same error rate as the SDP but can scale to much larger problems. We compare both SDP and l1-based approaches with classical line spectral analysis methods and demonstrate that the SDP outperforms the l1 optimization which outperforms MUSIC, Cadzow's, and Matrix Pencil approaches in terms of MSE over a wide range of signal-to-noise ratios.
527 citations
TL;DR: The spectral CS (SCS) recovery framework for arbitrary frequencysparse signals is introduced and it is demonstrated that SCS signicantly outperforms current state-of-the-art CS algorithms based on the DFT while providing provable bounds on the number of measurements required for stable recovery.
452 citations
Journal Article•
TL;DR: Though ESPRIT is discussed in the context of direction-of-arrival estimation, it can be applied to a wide variety of problems including spectral estimation and has several advantages over earlier techniques such as MUSIC including improved performance, reduced computational load, freedom from array characterization/calibration, and reduced sensitivity to array perturbations.
Abstract: A new approach to the general problem of signal parameter estimation is described. Though the technique ESPRIT is discussed in the context of direction-of arrival estimation, it can be applied to a wide variety of problems including spectral estimation. ESPRIT exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational in variance structure (e.g., pairwise matched and co-directional antenna element doublets) and has several advantages over earlier techniques such as MUSIC including improved performance, reduced computational load, freedom from array characterization calibration, and reduced sensitivity to array perturbations. Results of computer simulations carried out to evaluate the new algorithm arc presented.
274 citations
01 Oct 2013
TL;DR: A new algorithm to estimate a signal from its short-time Fourier transform modulus (STFTM) shows not only significant improvement in speed of convergence but it does as well recover the signals with a smaller error than the traditional GLA.
Abstract: In this paper, we present a new algorithm to estimate a signal from its short-time Fourier transform modulus (STFTM). This algorithm is computationally simple and is obtained by an acceleration of the well-known Griffin-Lim algorithm (GLA). Before deriving the algorithm, we will give a new interpretation of the GLA and formulate the phase recovery problem in an optimization form. We then present some experimental results where the new algorithm is tested on various signals. It shows not only significant improvement in speed of convergence but it does as well recover the signals with a smaller error than the traditional GLA.
128 citations
TL;DR: In order to reduce the influence of Heisenberg' s uncertainty, it is proposed that different signal components are windowed by different Gaussian windows, which brings better adaption and flexibility.
Abstract: This paper proposes a real-time power quality disturbances (PQDs) classification by using a hybrid method (HM) based on S-transform (ST) and dynamics (Dyn). Classification accuracy and run time are mainly considered in our work. The HM firstly uses Dyn to identify the location of the signal components in the frequency spectrum yielded by Fourier transform, and uses inverse Fourier transform to only some of the signal components. Then features from Fourier transform, ST, and Dyn are selected, and a decision tree is used to classify the types of PQD. In order to reduce the influence of Heisenberg' s uncertainty, we proposed that different signal components are windowed by different Gaussian windows, which brings better adaption and flexibility. By the HM, run time of the application has been greatly reduced with satisfactory classification accuracy. Finally, a DSP-FPGA based hardware platform is adopted to test the run time and correctness of the proposed method under real standard signals. Field signal tests have also presented. Both simulations and experiments validate the feasibility of the new method.
128 citations
TL;DR: The bias and mean square error (MSE) analysis of the frequency estimator suggested in is given and an improved version of the estimator, with the removal of estimator bias, is suggested.
Abstract: The bias and mean square error (MSE) analysis of the frequency estimator suggested in is given and an improved version of the estimator, with the removal of estimator bias, is suggested. The signal-to-noise ratio (SNR) threshold above which the bias removal is effective is also determined.
125 citations
Posted Content•
TL;DR: This paper establishes that using atomic norm soft thresholding (AST), it can achieve near minimax optimal prediction error rate for line spectral estimation, in spite of having a highly coherent dictionary corresponding to arbitrarily close frequencies.
Abstract: This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery problem with a continuous, infinite dictionary. We show how to compute the estimator via semidefinite programming and provide guarantees on its mean-square error rate. We derive a complementary minimax lower bound on this estimation rate, demonstrating that our approach nearly achieves the best possible estimation error. Furthermore, we establish bounds on how well our estimator localizes the frequencies in the signal, showing that the localization error tends to zero as the number of samples grows. We verify our theoretical results in an array of numerical experiments, demonstrating that the semidefinite programming approach outperforms two classical spectral estimation techniques.
123 citations
TL;DR: In this article, a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage is proposed, which can be interpreted as estimating the global power spectrum when only a portion of the data are available for analysis, or estimating the power spectra from local data under the assumption that the data data are locally stationary in a specified region.
Abstract: We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage. Our approach can be interpreted either as estimating the global power spectrum of a stationary process when only a portion of the data are available for analysis, or estimating the power spectrum from local data under the assumption that the data are locally stationary in a specified region. Restricting a global function to a spatial subdomain -- whether by necessity or by design -- is a windowing operation, and an equation like a convolution in the spectral domain relates the expected value of the windowed power spectrum to the underlying global power spectrum and the known power spectrum of the localization window. The best windows for the purpose of localized spectral analysis have their energy concentrated in the region of interest while possessing the smallest effective bandwidth as possible. Solving an optimization problem in the sense of Slepian (1960) yields a family of orthogonal windows of diminishing spatiospectral localization, the best concentrated of which we propose to use to form a weighted multitaper spectrum estimate in the sense of Thomson (1982). Such an estimate is both more representative of the target region and reduces the estimation variance when compared to estimates formed by any single bandlimited window. We describe how the weights applied to the individual spectral estimates in forming the multitaper estimate can be chosen such that the variance of the estimate is minimized.
101 citations
TL;DR: In this paper, the authors developed the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data, and derived an asymptotic Gaussian representation of the fDFT, thus allowing the transformation of the original collection of dependent random functions into a collection of approximately independent complexvalued Gaussian random functions.
Abstract: We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which generalises the notion of a spectral density matrix to the functional setting, and characterises the second-order dynamics of the process. Our main tool is the functional Discrete Fourier Transform (fDFT). We derive an asymptotic Gaussian representation of the fDFT, thus allowing the transformation of the original collection of dependent random functions into a collection of approximately independent complex-valued Gaussian random functions. Our results are then employed in order to construct estimators of the spectral density operator based on smoothed versions of the periodogram kernel, the functional generalisation of the periodogram matrix. The consistency and asymptotic law of these estimators are studied in detail. As immediate consequences, we obtain central limit theorems for the mean and the long-run covariance operator of a stationary functional time series. Our results do not depend on structural modelling assumptions, but only functional versions of classical cumulant mixing conditions, and are shown to be stable under discrete observation of the individual curves.
98 citations
TL;DR: The L-estimate transforms and time-frequency representations are presented within the framework of compressive sensing to recover signal or local auto-correlation function samples corrupted by impulse noise.
Abstract: The L-estimate transforms and time-frequency representations are presented within the framework of compressive sensing. The goal is to recover signal or local auto-correlation function samples corrupted by impulse noise. The signal is assumed to be sparse in a transform domain or in a joint-variable representation. Unlike the standard L-statistics approach, which suffers from degraded spectral characteristics due to the omission of samples, the compressive sensing in combination with the L-estimate permits signal reconstruction that closely approximates the noise free signal representation.
TL;DR: A fast and efficient algorithm based on the alternating split Bregman technique is proposed to carry out the optimization with computational complexity of time-frequency (TF) decomposition in the framework of sparse regularization theory.
Abstract: In this paper, time-frequency (TF) decomposition (TFD) is studied in the framework of sparse regularization theory. The short-time Fourier transform is first formulated as a convex constrained optimization where a mixed l1-l2 norm of the coefficients is minimized subject to a data fidelity constraint. Such formulation leads to a novel invertible decomposition with adjustable TF resolution. Then, a fast and efficient algorithm based on the alternating split Bregman technique is proposed to carry out the optimization with computational complexity [N2 log(N)]. Window length is a key parameter in windowed Fourier transform which affects the TF resolution; a novel method is also presented to determine the optimum window length for a given signal resulting to maximum compactness of energy in the TF domain. Numerical experiments show that the proposed sparsity-based TFD generates high-resolution TF maps for a wide range of signals having simple to complicated patterns in the TF domain. The performance of the proposed algorithm is also shown on real oil industry examples, such as ground roll noise attenuation and direct hydrocarbon detection from seismic data.
01 Oct 2013
TL;DR: In this paper, the authors presented the first sample-optimal sublinear time algorithms for the sparse Discrete Fourier Transform over a two-dimensional √ n × √n grid.
Abstract: We present the first sample-optimal sublinear time algorithms for the sparse Discrete Fourier Transform over a two-dimensional √n × √n grid. Our algorithms are analyzed for the average case signals. For signals whose spectrum is exactly sparse, we present algorithms that use O(k) samples and run in O(k log k) time, where k is the expected sparsity of the signal. For signals whose spectrum is approximately sparse, we have an algorithm that uses O(k log n) samples and runs in O(k log2 n) time, for k = Θ(√n). All presented algorithms match the lower bounds on sample complexity for their respective signal models.
TL;DR: A novel speed and position estimation method based on identification of rotor slot harmonics (RSH) that does not require any kind of spectral analysis is proposed and can be applied within a typical control cycle of a vector controlled drive algorithm.
Abstract: It is well known that slotting harmonics exist in most of the electrical machines. So far, these harmonics are mainly identified using spectral estimation techniques. However, this approach requires long sampling and computation periods. In this study, a novel speed and position estimation method based on identification of rotor slot harmonics (RSH) that does not require any kind of spectral analysis is proposed. The required information is extracted by demodulating the information available in an external search coil (or in phase current). The algorithm used for this purpose is fast and can be applied within a typical control cycle of a vector controlled drive algorithm. In the application of the method here, higher order RSH have been utilized. In this manner, the position estimation resolution increases and also possible effect of harmonics stemming from other sources are avoided. The approach is explained in the paper and illustrated with experimental results.
TL;DR: An adaptive technique based on estimation of signal parameters via rotational invariance technique (ESPRIT) is proposed that optimizes the accuracy and computation time for harmonic/interharmonic estimation of stationary as well as nonstationary power supply signals.
Abstract: Model-based parametric techniques offer many advantages over conventional discrete Fourier transform-based methods for harmonic/interharmonic estimation. However, high computational requirements restrict their applications to offline analysis purpose. In this paper, an adaptive technique based on estimation of signal parameters via rotational invariance technique (ESPRIT) is proposed that optimizes the accuracy and computation time for harmonic/interharmonic estimation of stationary as well as nonstationary power supply signals. This method first estimates the order of the model (number of sinusoids present in the distorted power supply signal) and then adjusts the autocorrelation matrix dimension based on reconstruction error. The performance of the proposed method is validated on the time-varying simulated signal, measured synthetic signal, and actual voltage signal of a distribution system supplying electric arc welding load. The comparison of the results with the short-time Fourier transform and the sliding window ESPRIT techniques shows that the proposed approach considerably reduces the computational time of high-resolution ESPRIT method along with better accuracy.
TL;DR: In this paper, the authors quantify the size of the uncertainty set using suitable notions of distance, and in particular to compute the diameter of the set since this represents an upper bound on the distance between any choice of a nominal element in the set and the true power spectrum.
Abstract: The purpose of this paper is to study metrics suitable for assessing uncertainty of power spectra when these are based on finite second-order statistics. The family of power spectra which is consistent with a given range of values for the estimated statistics represents the uncertainty set about the “true” power spectrum. Our aim is to quantify the size of this uncertainty set using suitable notions of distance, and in particular, to compute the diameter of the set since this represents an upper bound on the distance between any choice of a nominal element in the set and the “true” power spectrum. Since the uncertainty set may contain power spectra with lines and discontinuities, it is natural to quantify distances in the weak topology-the topology defined by continuity of moments. We provide examples of such weakly continuous metrics and focus on particular metrics for which we can explicitly quantify spectral uncertainty. We then consider certain high resolution techniques which utilize filter-banks for preprocessing, and compute worst case a priori uncertainty bounds solely on the basis of the filter dynamics. This allows the a priori tuning of the filter-banks for improved resolution over selected frequency bands.
26 May 2013
TL;DR: A greedy recovery algorithm is introduced that leverages a band-exclusion function and a polar interpolation function to address two issues in spectral compressive sensing of frequency-sparse signals.
Abstract: Existing approaches to compressive sensing of frequency-sparse signals focuses on signal recovery rather than spectral estimation. Furthermore, the recovery performance is limited by the coherence of the required sparsity dictionaries and by the discretization of the frequency parameter space. In this paper, we introduce a greedy recovery algorithm that leverages a band-exclusion function and a polar interpolation function to address these two issues in spectral compressive sensing. Our algorithm is geared towards line spectral estimation from compressive measurements and outperforms most existing approaches in fidelity and tolerance to noise.
TL;DR: This paper introduces a Discrete Fourier Transform (DFT)-based algorithm to extract the Electric Network Frequency (ENF) information from an audio recording for use in audio authentication.
Abstract: This paper introduces a Discrete Fourier Transform (DFT)-based algorithm to extract the Electric Network Frequency (ENF) information from an audio recording for use in audio authentication. The basic idea of the proposed algorithm is to calculate the specific spectral lines by DFT in the frequency domain at the desired frequency point instead of throughout the entire frequency band. Then a binary search technique is employed to search the next desired frequency bin to repeat the spectral line calculation until the hidden ENF information is extracted. The purpose is to improve the accuracy and precision of conventional ENF extraction methods and also to enhance the calculation efficiency. Both simulated audio signals with different signal-to-noise ratios (SNRs) and actual audio recordings are studied to verify the performance of the proposed algorithm. Two error-evaluation criteria, frequency offset and frequency bias, are defined to evaluate the algorithm performance on accuracy and precision. The test results and the error evaluation prove the validation and demonstrate the improvement of the proposed algorithm.
20 Mar 2013
TL;DR: In this article, the authors used atomic norm soft thresholding (AST) to obtain a near minimax optimal prediction error rate for line spectral estimation, in spite of having a highly coherent dictionary corresponding to arbitrarily close frequencies.
Abstract: Line spectral estimation is a classical signal processing problem involving estimation of frequencies and amplitudes from noisy equispaced samples of a sparse combination of complex sinusoids. We view this as a sparse recovery problem with a continuous, infinite dictionary, and employ tools from convex optimization for estimation. In this paper, we establish that using atomic norm soft thresholding (AST), we can achieve near minimax optimal prediction error rate for line spectral estimation, in spite of having a highly coherent dictionary corresponding to arbitrarily close frequencies. We also derive guarantees on the frequency localization performance of AST.
TL;DR: This study focused on processing signals in substation automation systems that comply with IEC 61850 by presenting high-accuracy frequency, amplitude, and phase estimation methods for asynchronous sampling based on phase difference estimation, compensation of number of samples, and a modified discrete Fourier transform.
Abstract: High-accuracy frequency, amplitude, and phase estimation methods for asynchronous sampling are presented. The proposed estimation methods are based on phase difference estimation, compensation of number of samples, and a modified discrete Fourier transform. This study focused on processing signals in substation automation systems that comply with IEC 61850. Some simulation tests were conducted in cases of pure and distorted sinusoids, and the frequency, amplitude, and phase errors of the fundamental and harmonics are evaluated at fundamental frequencies around 50 Hz at fixed sampling rates of 4 kHz and 12.8 kHz (i.e., 80 and 256 samples per period). Dependence of each estimation accuracy on a fraction of number of samples is discussed.
TL;DR: The authors have used decimated Pade approximant (DPA), where the input time signal points or auto-correlation functions are given via measurements or computations, and the task is to reconstruct the unknown components as the harmonic variables in terms of the fundamental complex frequencies and amplitudes.
Abstract: Although today water is becoming more and more precious, its major waste is caused by transportation. The authorities in charge of the management of water pipes indicate double-digit percentage of waste, sometimes it even exceeds 50% the amount of water mostly lost by inefficiency of distribution waterworks. In this study, the authors present an alternative method of spectral analysis, used for detecting leaks in water pipes, with respect to classical spectral methods as direct Fourier transform/fast Fourier transform. They have used decimated Pade approximant (DPA), where the input time signal points or auto-correlation functions are given via measurements or computations, and the task is to reconstruct the unknown components as the harmonic variables in terms of the fundamental complex frequencies and amplitudes. They have also introduced decimated linear predictor technique as direct consequence of the DPA, since they differ only in one step, namely the calculation of the amplitudes.
TL;DR: Algorithms for fast measurement and the nonparametric estimation of the unknown changing frequency, amplitude, and phase difference of the signals from two channels with the same frequency, as well as other power quantities, such as the apparent, the active, and the reactive power are presented.
Abstract: This paper presents algorithms for fast measurement and the nonparametric estimation of the unknown changing frequency, amplitude, and phase difference of the signals from two channels with the same frequency, as well as other power quantities, such as the apparent, the active, and the reactive power. The possibilities for systematic error reduction through use of the interpolated discrete Fourier transform using the Rife-Vincent windows class I (RV-I) are described. RV-I windows are designed for maximization of the window spectrum side-lobes fall-off and owing to their minimal leakage, minimal systematic bias curves can be evaluated as a function of the measurement interval duration expressed in signal cycles. Parameters are calculated from the discrete Fourier transform coefficients around the component peaks by summation to reduce the leakage effects. The optimum for reducing the time of measurement and for reducing systematic errors under non-coherent conditions of sampling real noisy signals could be the estimation with the three cycles window using the three-point interpolation and the RV-I window order 3.
TL;DR: This work proposes a compressive estimator of the discrete Rihaczek spectrum (RS), which combines a minimum variance unbiased estimators of the RS with a compressed sensing technique that exploits the approximate time-frequency sparsity.
Abstract: Estimating the spectral characteristics of a nonstationary random process is an important but challenging task, which can be facilitated by exploiting structural properties of the process. In certain applications, the observed processes are underspread, i.e., their time and frequency correlations exhibit a reasonably fast decay, and approximately time-frequency sparse, i.e., a reasonably large percentage of the spectral values are small. For this class of processes, we propose a compressive estimator of the discrete Rihaczek spectrum (RS). This estimator combines a minimum variance unbiased estimator of the RS (which is a smoothed Rihaczek distribution using an appropriately designed smoothing kernel) with a compressed sensing technique that exploits the approximate time-frequency sparsity. As a result of the compression stage, the number of measurements required for good estimation performance can be significantly reduced. The measurements are values of the ambiguity function of the observed signal at randomly chosen time and frequency lag positions. We provide bounds on the mean-square estimation error of both the minimum variance unbiased RS estimator and the compressive RS estimator, and we demonstrate the performance of the compressive estimator by means of simulation results. The proposed compressive RS estimator can also be used for estimating other time-dependent spectra (e.g., the Wigner-Ville spectrum), since for an underspread process most spectra are almost equal.
16 Jun 2013
TL;DR: In this article, two non-parametric spectral estimators focusing on mode frequency estimation are applied to synchrophasor data to provide valuable information about lightly damped low-frequency modes in power systems.
Abstract: Spectral analysis applied to synchrophasor data can provide valuable information about lightly damped low-frequency modes in power systems. This paper demonstrates application of two non-parametric spectral estimators focusing on mode frequency estimation. The first one is the well-known Welch spectral estimator whereas the application of Multitaper method is proposed here. In addition, the paper discusses mode estimator tuning procedures and the estimators' performances in the presence of “forced” oscillations. The validity of the proposed application of the non-parametric estimators and tuning procedures is verified through both simulated data and PMU data originating from the high-voltage grid of the Nordic power system. Special attention is given to the analysis of the behaviour of different low frequency modes present in the Nordic grid, including that of forced oscillations.
TL;DR: In this paper, an analytical method based on 3-D Fourier integral was proposed to obtain accurate spectra of both the switching functions and the synthesized terminal quantities of a matrix converter.
Abstract: This letter proposes an analytical method based on 3-D Fourier integral to obtain accurate spectra of both the switching functions and the synthesized terminal quantities of a matrix converter. The challenges associated with the spectral analysis of matrix converter waveforms are twofold. On one hand, the modulation signal contains both the input and output frequencies. Unlike the third-harmonic injection in the modulation functions, the input frequency and the output frequency are typically independent from each other and will not form an integer ratio. On the other hand, it is very common that the switching frequency or the carrier frequency is not rational multiple of either the input frequency or the output frequency. These aforementioned challenges make it a very challenging task to accurately characterize the spectra of matrix converter waveforms through commonly resorted numerical methods such as a fast Fourier transform (FFT). The contribution of the proposed analytical method lies in providing accurate solution to spectral analysis of matrix converters when the FFT approach fails to characterize the spectral performance of matrix converters under typical operating conditions.
TL;DR: This paper presents a text-independent speaker recognition technique in which the conventional Fourier transform in Mel-Frequency Cepstral Coefficient front-end is substituted by fractional Fourier Transform, making the technique robust against additive noise compared to Fourier domain maintaining same computational complexity.
TL;DR: It is demonstrated that, by proper dimensioning the signal subspace, the MUSIC algorithm can be optimized in order to accurately assess the heart rate during an 8-28 s time interval.
Abstract: Non-contact methods for the assessment of vital signs are of great interest for specialists due to the benefits obtained in both medical and special applications, such as those for surveillance, monitoring, and search and rescue. This paper investigates the possibility of implementing a digital processing algorithm based on the MUSIC (Multiple Signal Classification) parametric spectral estimation in order to reduce the observation time needed to accurately measure the heart rate. It demonstrates that, by proper dimensioning the signal subspace, the MUSIC algorithm can be optimized in order to accurately assess the heart rate during an 8–28 s time interval. The validation of the processing algorithm performance was achieved by minimizing the mean error of the heart rate after performing simultaneous comparative measurements on several subjects. In order to calculate the error the reference value of heart rate was measured using a classic measurement system through direct contact.
TL;DR: A novel block prior is proposed for adaptive Bayesian estimation that puts sufficient prior mass near the true signal and automatically concentrates on its effective dimension.
Abstract: A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its effective dimension. A rate-optimal posterior contraction is obtained in a general framework, which includes density estimation, white noise model, Gaussian sequence model, Gaussian regression and spectral density estimation.
TL;DR: S-transform as discussed by the authors is a new time-frequency analysis method, which is deduced from short-time Fourier transform and continue Wavelet transform, and it has much better performance than traditional timefrequency method.
Abstract: S-transform is a new time-frequency analysis method, which is deduced from short-time Fourier transform and continue Wavelet transform. It has much better performance than traditional time-frequency method. Therefore, in this paper, the basic principle of is briefly introduced and the relationships between is analyzed by theoretical derivation. According to the simulation experiments, the time-frequency space characteristics of short-time Fourier transform, Wigner-Ville distribution and S-transform are contrasted. As the results shown, the window of S-transform has a progressive frequency dependent resolution. So the Stransform has a great flexibility and utility in the processing of non-stationary signal. Compare with the time-frequency spectrum of three different analysis methods under various noise conditions, it is obvious that S-transform has much better anti-noise performance than that of traditional methods for non-stationary signal processing. Based on the superior timefrequency resolution, the S-transform spectrum can be used to describe the structure of incoming signal effectively.
TL;DR: In this article, the authors considered a continuous-time autoregressive moving average (CARMA) process driven by either a symmetric α-stable Levy process with α ∈ 0,2 or a finite second moments and established a consistent estimate for the normalized power transfer function by applying a smoothing filter to the periodogram.
Abstract: In this article, we consider a continuous-time autoregressive moving average (CARMA) process driven by either a symmetric α-stable Levy process with α ∈ (0,2) or a symmetric Levy process with finite second moments. In the asymptotic framework of high-frequency data within a long time interval, we establish a consistent estimate for the normalized power transfer function by applying a smoothing filter to the periodogram of the CARMA process. We use this result to propose an estimator for the parameters of the CARMA process and exemplify the estimation procedure by a simulation study.