Showing papers on "Spectral density estimation published in 2016"

Super-Resolution Compressed Sensing for Line Spectral Estimation: An Iterative Reweighted Approach

Abstract: Conventional compressed sensing theory assumes signals have sparse representations in a known dictionary. Nevertheless, in many practical applications such as line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional compressed sensing technique to such applications, the continuous parameter space has to be discretized to a finite set of grid points, based on which a “nominal dictionary” is constructed for sparse signal recovery. Discretization, however, inevitably incurs errors since the true parameters do not necessarily lie on the discretized grid. This error, also referred to as grid mismatch, leads to deteriorated recovery performance. In this paper, we consider the line spectral estimation problem and propose an iterative reweighted method which jointly estimates the sparse signals and the unknown parameters associated with the true dictionary. The proposed algorithm is developed by iteratively decreasing a surrogate function majorizing a given log-sum objective function, leading to a gradual and interweaved iterative process to refine the unknown parameters and the sparse signal. A simple yet effective scheme is developed for adaptively updating the regularization parameter that controls the tradeoff between the sparsity of the solution and the data fitting error. Theoretical analysis is conducted to justify the proposed method. Simulation results show that the proposed algorithm achieves super resolution and outperforms other state-of-the-art methods in many cases of practical interest.

STFT Phase Retrieval: Uniqueness Guarantees and Recovery Algorithms

Abstract: The problem of recovering a signal from its Fourier magnitude is of paramount importance in various fields of engineering and applied physics. Due to the absence of Fourier phase information, some form of additional information is required in order to be able to uniquely, efficiently, and robustly identify the underlying signal. Inspired by practical methods in optical imaging, we consider the problem of signal reconstruction from the short-time Fourier transform (STFT) magnitude. We first develop conditions under, which the STFT magnitude is an almost surely unique signal representation. We then consider a semidefinite relaxation-based algorithm (STliFT) and provide recovery guarantees. Numerical simulations complement our theoretical analysis and provide directions for future work.

Radar High-Speed Target Detection Based on the Frequency-Domain Deramp-Keystone Transform

Abstract: In this paper, we propose a coherent detection algorithm for high-speed targets by employing the parametric symmetric autocorrelation function and the frequency-domain deramp-keystone transform (FDDKT). This coherent detection algorithm is an extension of the scaled inverse Fourier transform (SCIFT)-based detection algorithm. However, compared to the SCIFT-based detection algorithm, the proposed coherent detection algorithm can acquire a better antinoise performance and higher peak to sidelobe ratios along the Doppler frequency and the scaled range cell. Simulations and analyses for synthetic models and the real radar data are provided to verify the effectiveness of the proposed coherent detection algorithm.

Induction Machines Fault Detection Based on Subspace Spectral Estimation

Abstract: The main objective of this paper is to detect faults in induction machines using a condition monitoring architecture based on stator current measurements. Two types of fault are considered: bearing and broken rotor bars faults. The proposed architecture is based on high-resolution spectral analysis techniques also known as subspace techniques. These frequency estimation techniques allow to separate frequency components including frequencies close to the fundamental one. These frequencies correspond to fault sensitive frequencies. Once frequencies are estimated, their corresponding amplitudes are obtained by using the least squares estimator. Then, a fault severity criterion is derived from the amplitude estimates. The proposed methods were tested using experimental stator current signals issued from two induction motors with the considered faults. The experimental results show that the proposed architecture has the ability to efficiently and cost-effectively detect faults and identify their severity.

Recent Developments in Speech Enhancement in the Short-Time Fourier Transform Domain

Abstract: In this paper, we present an overview on the topic of noise reduction in the short-time Fourier transform (STFT) domain. First, we briefly review the conventional literature in the single- and multichannel cases separately. In the single-channel scenario, we focus on the spectral subtractive methods, Wiener filter based methods, speech amplitude estimators and estimators of the complex STFT coefficients. In the multi-channel scenario, we investigate in short a selection of key beamforming approaches as well as conventional post-filtering methods. Next, a detailed survey of the most recent advances in the STFT-based noise reduction methods is provided. This includes STSA estimators with super-Gaussian priors, noise power spectral density (PSD ) estimation, estimation methods in the modulation domain, estimation of spectral phase and noise PSD matrix estimation for multi-channel applications. Finally, we summarize the presented material and draw important conclusions on each of the investigated topics.

Identification of Electromechanical Modes Based on the Digital Taylor-Fourier Transform

Abstract: The digital Taylor-Fourier transform (DTFT) is used to identify low-frequency electromechanical modes in power systems. The identification process is based on the time-frequency analysis of nonlinear signals that arise after a large disturbance. The DTFT creates a signal decomposition, from which mono-component signals are extracted by spectral analysis using a filter bank. This analysis is accomplished through sliding-window data, which is updated each sample, yielding estimates of the reconstructed signal and providing information of its instantaneous damping and frequency. Results demonstrate the applicability of the proposition.

Bi-Directional Algorithm for Computing Discrete Spectral Amplitudes in the NFT

Abstract: The nonlinear Fourier transform represents a signal in terms of its continuous spectrum, discrete eigenvalues, and the corresponding discrete spectral amplitudes. This paper presents a new bi-directional algorithm for computing the discrete spectral amplitudes, which addresses the significant problem of rounding errors inherent in previously known techniques. We use the proposed method to obtain accurate spectral-domain noise statistics for 2-soliton signals using numerical simulation.

A New and Accurate Estimator With Analytical Expression for Frequency Estimation

Abstract: Frequency estimation of a single complex exponential waveform is an important problem in many fields. In this letter, a new frequency estimator for a complex exponential sine waveform observed under the additive white Gaussian noise (AWGN) is proposed. The proposed estimator is obtained by solving the nonlinear functions. The new estimator has an analytical expression based on interpolation method with three DFT samples. Numerical results demonstrate that the performance of the proposed estimator has lower SNR threshold to closely reach the Cramer-Rao bound (CRB) in the low SNR region and its performance also outperforms previous estimators in the high SNR region.

Vital-Sign Extraction Using Bootstrap-Based Generalized Warblet Transform in Heart and Respiration Monitoring Radar System

Abstract: In biomedical Doppler radar applications, the return signal is a nonlinear frequency-modulation (NLFM) random process whose phase conveys heart and respiration vital-sign information. These signatures modulate the phase of the signal as two oscillating components with frequencies less than a few hertz. Due to the nonstationary nature of these signals, their analysis by 1-D techniques, temporal and spectral, may not be very useful, and time-frequency techniques may be incapable of accurately extracting their instantaneous frequency (IF) trajectory. In this paper, we present a bootstrap-based generalized warblet transform (GWT) signal processing method. The presented signal processing tool is a parametric method that has a kernel with Fourier-series components. The coefficients of the kernel are estimated by an iteration procedure that converges to the IF of the radar signal. We show theoretically and experimentally that the bootstrap-based GWT can extract the amplitude and frequency of the two vital-sign components at a range of 3 m in the face of low signal-to-noise ratio and in the presence of phase noise and body motion artifacts, achieving an accuracy that is potentially better than conventional methods can provide.

An Accurate Method for Frequency Estimation of a Real Sinusoid

Abstract: It is well known that the positive- and negative-frequency components of a real sinusoid spectrally interact with each other; thus, introducing bias in frequency estimation based on the periodogram maximization. We propose to filter out the negative-frequency component. To that end, a coarse frequency estimation is obtained using the windowing approach, known to reduce the estimation bias, and then used to filter out the negative-frequency component via modulation and discrete Fourier transform bin excision approach. Fine estimation is performed using accurate frequency estimators, developed for complex sinusoids, on the filtered signal. The proposed method is characterized by the $ O(N\log _2N)$ complexity in terms of additions/multiplications and the $ O(N)$ complexity in terms of sine/cosine operations and comparisons. Moreover, it achieves the Cramer–Rao lower bound and is not sensitive to sinusoid frequency and initial phase, thus, outperforming the state-of-the-art methods.

Minimax adaptive estimation of nonparametric hidden Markov models

Abstract: We consider stationary hidden Markov models with finite state space and nonparametric modeling of the emission distributions. It has remained unknown until very recently that such models are identifiable. In this paper, we propose a new penalized least-squares estimator for the emission distributions which is statistically optimal and practically tractable. We prove a non asymptotic oracle inequality for our nonparametric estimator of the emission distributions. A consequence is that this new estimator is rate minimax adaptive up to a logarithmic term. Our methodology is based on projections of the emission distributions onto nested subspaces of increasing complexity. The popular spectral estimators are unable to achieve the optimal rate but may be used as initial points in our procedure. Simulations are given that show the improvement obtained when applying the least-squares minimization consecutively to the spectral estimation.

Three-Phase Harmonic and Sequence Components Measurement Method Based on mSDFT and Variable Sampling Period Technique

Abstract: This paper presents a three-phase harmonic and sequence components measurement method based on modulated sliding discrete Fourier transform (mSDFT) and a variable sampling period technique. The proposal allows measuring the harmonic components of a three-phase signal and computes the corresponding imbalance by estimating the instantaneous symmetrical components. In addition, an adaptive variable sampling period is used to obtain a sampling frequency multiple of the main frequency. By doing so, DFT typical errors, known as spectral leakage and picket-fence effect, are mitigated in steady state. The proposal is tested with different disturbances by simulation and experimental results. Some results obtained with a power quality monitor implemented with the proposed system are also presented. The high rejection to distortion in the electrical network, frequency adaptability, flexibility, and good performance in power quality monitor application render the proposed method a promising alternative for signal processing from the mains.

Compressive Spectral Estimation with Single-Snapshot ESPRIT: Stability and Resolution

Abstract: In this paper Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) is developed for spectral estimation with single-snapshot measurement. Stability and resolution analysis with performance guarantee for Single-Snapshot ESPRIT (SS-ESPRIT) is the main focus. In the noise-free case, exact reconstruction is guaranteed for any arbitrary set of frequencies as long as the number of measurement data is at least twice the number of distinct frequencies to be recovered. In the presence of noise and under the assumption that the true frequencies are separated by at least two times Rayleigh's Resolution Length, an explicit error bound for frequency reconstruction is given in terms of the dynamic range and the separation of the frequencies. The separation and sparsity constraint compares favorably with those of the leading approaches to compressed sensing in the continuum.

Efficient Spectral Estimation by MUSIC and ESPRIT with Application to Sparse FFT

Abstract: In spectral estimation, one has to determine all parameters of an exponential sum for finitely many (noisy) sampled data of this exponential sum. Frequently used methods for spectral estimation are MUSIC (MUltiple SIgnal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique). For a trigonometric polynomial of large sparsity, we present a new sparse fast Fourier transform by shifted sampling and using MUSIC resp. ESPRIT, where the ESPRIT based method has lower computational cost. Later this technique is extended to a new reconstruction of a multivariate trigonometric polynomial of large sparsity for given (noisy) values sampled on a reconstructing rank-1 lattice. Numerical experiments illustrate the high performance of these procedures.

Approximate support recovery of atomic line spectral estimation: A tale of resolution and precision

Abstract: This work investigates the parameter estimation performance of line spectral estimation/super-resolution using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes from noisy observations. When the Signal-to-Noise Ratio is reasonably high and the true frequencies are separated by O(1/n), the atomic norm estimator is shown to localize the correct number of frequencies, each within a neighborhood of size O(√log n/n3 σ) of one of the true frequencies. Here n is half the number of temporal samples and σ2 is the Gaussian noise variance. The analysis is based on a primal-dual witness construction procedure. The error bound obtained matches the Cramer-Rao lower bound up to a logarithmic factor. The relationship between resolution (separation of frequencies) and precision/accuracy of the estimator is highlighted.

Discrete Fourier Transform Method for Discrimination of Digital Scintillation Pulses in Mixed Neutron-Gamma Fields

Abstract: A discrete Fourier transform method (DFTM) for discrimination between the signal of neutrons and gamma rays in organic scintillation detectors is presented. The method is based on the transformation of signals into the frequency domain using the sine and cosine Fourier transforms in combination with the discrete Fourier transform. The method is largely benefited from considerable differences that usually is available between the zero-frequency components of sine and cosine and the norm of the amplitude of the DFT for neutrons and gamma-ray signals. Moreover, working in frequency domain naturally results in considerable suppression of the unwanted effects of various noise sources that is expected to be effective in time domain methods. The proposed method could also be assumed as a generalized nonlinear weighting method that could result in a new class of pulse shape discrimination methods, beyond definition of the DFT. A comparison to the traditional charge integration method (CIM), as well as the frequency gradient analysis method (FGAM) and the wavelet packet transform method (WPTM) has been presented to demonstrate the applicability and efficiency of the method for real-world applications. The method, in general, shows better discrimination Figure of Merits (FoMs) at both the low-light outputs and in average over the studied energy domain. A noise analysis has been performed for all of the abovementioned methods. It reveals that the frequency domain methods (FGAM and DFTM) are less sensitive to the noise effects.

On Robust Estimation of Power Spectra

Abstract: Let us consider the problem of robust spectral density estimation. Conventional methods to obtain estimates of spectral density function are not robust in the presence of outlying observations. We present different methods to robustly estimate the spectral density function that are insensitive against outliers. The proposed methods are applied to simulated and real data and the results are compared. As a special practical application we focus on the frequency-domain analysis of short-term heart rate variability measurements of diabetes patients.

Automatic human fall detection in fractional fourier domain for assisted living

Abstract: Fast and accurate detection of elderly falls can significantly reduce the rate of morbidity and mortality. In the past decade, extensive research has been performed to achieve real-time fall monitoring solutions. In this paper, we consider the radar-based modality and utilize the family of fractional Fourier transform to enhance the motion Doppler signature of falls. Compare with the conventional time-frequency analysis approaches, the proposed method achieves higher signal energy concentration and thus yields improved fall detection in low signal-to-noise ratio scenarios. Experimental results are used to validate the theoretical analysis and to demonstrate the feasibility of the proposed approach.

Voyager 2 solar plasma and magnetic field spectral analysis for intermediate data sparsity

Abstract: The Voyager probes are the furthest, still active, spacecraft ever launched from Earth. During their 38 year trip, they have collected data regarding solar wind properties (such as the plasma velocity and magnetic field intensity). Unfortunately, a complete time evolution of the measured physical quantities is not available. The time series contains many gaps which increase in frequency and duration at larger distances. The aim of this work is to perform a spectral and statistical analysis of the solar wind plasma velocity and magnetic field using Voyager 2 data measured in 1979, when the gap density is between the 30% and 50%. For these gap densities, we show the spectra of gapped signals inherit the characteristics of the data gaps. In particular, the algebraic decay of the intermediate frequency range is underestimated and discrete peaks result not from the underlaying data but from the gap sequence. This analysis is achieved using five different data treatment techniques coming from the multidisciplinary context: averages on linearly interpolated subsets, correlation without data interpolation, correlation of linearly interpolated data, maximum likelihood data reconstruction, and compressed sensing spectral estimation. With five frequency decades, the spectra we obtained have the largest frequency range ever computed at five astronomical units from the Sun; spectral exponents have been determined for all the components of the velocity and magnetic field fluctuations. Void analysis is also useful in recovering other spectral properties such as micro and integral scales.

Approximate Support Recovery of Atomic Line Spectral Estimation: A Tale of Resolution and Precision.

Abstract: This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes from noisy observations. When the Signal-to-Noise Ratio is reasonably high and the true frequencies are separated by $O(\frac{1}{n})$, the atomic norm estimator is shown to localize the correct number of frequencies, each within a neighborhood of size $O(\sqrt{{\log n}/{n^3}} \sigma)$ of one of the true frequencies. Here $n$ is half the number of temporal samples and $\sigma^2$ is the Gaussian noise variance. The analysis is based on a primal-dual witness construction procedure. The obtained error bound matches the Cramer-Rao lower bound up to a logarithmic factor. The relationship between resolution (separation of frequencies) and precision or accuracy of the estimator is highlighted. Our analysis also reveals that the atomic norm minimization can be viewed as a convex way to solve a $\ell_1$-norm regularized, nonlinear and nonconvex least-squares problem to global optimality.

Time-Frequency analysis via the Fourier Representation

Abstract: The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the inverse Fourier transform. This study presents time-frequency analysis by the Fourier transform which maps the time-domain signal into the frequency-domain. In this study, we derive the time information from the phase of the frequency-domain signal and obtain the time-frequency representation. In order to obtain the time information in Fourier domain, we define the concept of 'frequen-taneous time' which is frequency derivative of phase. This is very similar to the group delay, which is also defined as frequency derivative of phase and it provide physical meaning only when it is positive. The frequen-taneous time is always positive or negative depending upon whether signal is defined for only positive or negative times, respectively. If a signal is defined for both positive and negative times, then we divide the signal into two parts, signal for positive times and signal for negative times. The proposed frequentaneous time and Fourier transform based time-frequency distribution contains only those frequencies which are present in the Fourier spectrum. Simulations and numerical results , on many simulated as well as read data, demonstrate the efficacy of the proposed method for the time-frequency analysis of a signal.

2D Discrete Fourier Transform with Simultaneous Edge Artifact Removal for Real-Time Applications

Abstract: Two-Dimensional (2D) Discrete Fourier Transform (DFT) is a basic and computationally intensive algorithm, with a vast variety of applications. 2D images are, in general, non-periodic, but are assumed to be periodic while calculating their DFTs. This leads to cross-shaped artifacts in the frequency domain due to spectral leakage. These artifacts can have critical consequences if the DFTs are being used for further processing. In this paper we present a novel FPGA-based design to calculate high-throughput 2D DFTs with simultaneous edge artifact removal. Standard approaches for removing these artifacts using apodization functions or mirroring, either involve removing critical frequencies or a surge in computation by increasing image size. We use a periodic-plus-smooth decomposition based artifact removal algorithm optimized for FPGA implementation, while still achieving real-time ($\ge$23 frames per second) performance for a 512$\times$512 size image stream. Our optimization approach leads to a significant decrease in external memory utilization thereby avoiding memory conflicts and simplifies the design. We have tested our design on a PXIe based Xilinx Kintex 7 FPGA system communicating with a host PC which gives us the advantage to further expand the design for industrial applications.

Robust fine acquisition algorithm for GPS receiver with limited resources

Abstract: The signal acquisition stage of a GPS receiver detects GPS satellites in view and provides coarse estimate of the GPS signal Doppler frequency shift and code delay for use by the tracking loops. The accuracy of the signal acquisition has a direct influence on the tracking performance. The implementation of a GPS signal acquisition algorithm requires compromising between acquisition frequency resolution improvement and reduction in acquisition time. A robust fine acquisition method is proposed to acquire the carrier frequency accurately after the completion of the coarse acquisition of the GPS signals. The proposed method uses Gram-Schmidt orthogonalization to provide robust spectral estimation of satellite Doppler frequency with less computational time. The proposed method starts after the coarse acquisition has been accomplished. The C/A code phase is striped off from the carrier signal. Then, sinusoidal candidate functions are generated at each of the frequencies range of interest, which is typically set around the estimated Doppler shift acquired from the coarse acquisition stage. Finally, an orthogonal search algorithm is utilized to detect the carrier frequency accurately. The performance of the proposed method is evaluated against of the computational load and the effects of the noise. Its performance was also compared to the state-of-the-art FFT and zero-padding FFT-based fine acquisition algorithms. The simulation and experimental results show that the proposed method outperforms existing methods and has sufficient acquisition accuracy for its application in the real world.