Frequency Estimation Of Signals Research Articles

RANSAC algorithm for instantaneous frequency estimation and reconstruction of frequency-modulated undersampled signals

Frequency modulated (FM) signals sampled below the Nyquist rate or with missing samples (nowadays part of wider compressive sensing (CS) framework) are considered. Recently proposed matching pursuit and greedy techniques are inefficient for signals with several phase parameters since they require a search over multidimensional space. An alternative is proposed here based on the random samples consensus algorithm (RANSAC) applied to the instantaneous frequency (IF) estimates obtained from the time-frequency (TF) representation of recordings (undersampled or signal with missing samples). The O’Shea refinement strategy is employed to refine results. The proposed technique is tested against third- and fifth-order polynomial phase signals (PPS) and also for signals corrupted by noise.

Interval frequency estimation by cross-correlation analysis

This paper presents a substantiation of interval frequency estimation which can be carried out based on frequency dependence of calculated values of cross-correlation coefficient between analyzed signal and reference sine function with zero initial phase. In considered approach the interval of frequencies which contains the exact frequency of analyzed signal is established by finding the range of frequencies limited by the maximum value of the main lobe and the closest zero crossing of this lobe. The results of carried out simulations for interval frequency estimation of a multifrequency signal are also given.

Frequency estimation of chirp signals based on fractional fourier transform combined with Otsu’s method

The parameters estimation of linear frequency modulation (LFM) signals, which also called chirp signals, have been widely applied in optical communication, LIDAR and many other fields. Fractional Fourier transform (FRFT) is one of the most important methods for estimating the frequency of chirp signals. However, the traditional estimation methods based on FRFT are incapable of high-precision parameter estimation for chirp signals, especially multi-component LFM signals. Therefore, we present a novel parameter estimation method based on the Otsu ratio, i.e., the interclass ratio of impulse signal to noise. An algorithm is used to determine this ratio, and then the frequency parameters of chirp signals are estimated by using the ratio as the fitness function. The parameter estimation of single-component and multi-component chirp signals is simulated. The results show that the proposed method has higher estimation accuracy than the traditional FRFT method.

A Passive DOA Estimation Algorithm of Underwater Multipath Signals via Spatial Time-Frequency Distributions

Direction of arrival (DOA) estimation of underwater multipath signals has become an indispensable part of many military and civil applications in the oceanic field. However, DOAs of different paths of the multipath signals may be the same or too close to be separated in space, which brings a great challenge to the DOA estimation of multipath signals. Besides, the number of multipath is generally unknown and time-varying in passive scenarios which generally lead to an underdetermined case. Therefore, it is essential to study an efficient algorithm to realize the underdetermined DOA estimation of underwater multipath signals in passive scenarios. This paper proposes a passive DOA estimation algorithm of underwater multipath signals via spatial time-frequency distributions (STFDs). Firstly, we establish a multipath signals model and utilize the quadratic time-frequency (TF) analysis method to reduce cross-terms while keeping a good resolution. Then, we estimate the number of multipath and introduce a novel multi-ridge detection technique to extract the TF trajectories of multipath signals, which adopts the idea of smoothing forward and backward, and the edge TF point detection strategy. Lastly, we estimate the DOA of each path of the multipath signals separately and realize source association based on the clustering-based method. Simulation results and analysis demonstrate that this algorithm can effectively improve the estimation accuracy of instantaneous frequency (IF) and DOA estimation of underwater multipath signals in underdetermined cases and passive situations.

A novel adaptive resampling for sequential Bayesian filtering to improve frequency estimation of time-varying signals

This paper presents a new algorithm for adaptive resampling, called percentile-based resampling (PBR) in a sequential Bayesian filtering, i.e., particle filter (PF) in particular, to improve tracking quality of the frequency trajectories under noisy environments. Since the conventional resampling scheme used in the PF suffers from computational burden, resulting in less efficiency in terms of computation time and complexity as well as the real time applications of the PF. The strategy to remedy this issue is proposed in this work. After state updating, important high particle weights are used to formulate the pre-set percentile in each sequential iteration to create a new set of high quality particles for the next filtering stage. The number of particles after PBR remains the same as the original. To verify the effectiveness of the proposed method, we first evaluated the performance of the method via numerical examples to a complex and highly nonlinear benchmark system. Then, the proposed method was implemented for frequency estimation for two time-varying signals. From the experimental results, via three measurement metrics, our approach delivered better performance than the others. Frequency estimates obtained by our method were excellent as compared to the conventional resampling method when number of particles were identical. In addition, the computation time of the proposed work was faster than those recent adaptive resampling schemes in literature, emphasizing the superior performance to the existing ones.

Scaled Wigner distribution using fractional instantaneous autocorrelation

The traditional Wigner distribution (WD) is extended to a novel one inspired by the definition of fractional bispectrum, giving rise to a scaled version with respect to the frequency variable, termed as the scaled Wigner distribution (SWD). A natural magnification effect characterized by a factor k on the frequency axis enables the SWD to have flexibility to be used in cross-term reduction. Some essential properties of this variation generalize very nicely and simply the classical results for the WD, and it enjoys a computational complexity in the order of O(kN2) comparable to O(N2) of the WD. The SWD does not use localization windows, but its resolutions depend on the factor k. Comparison of the detection performance (i.e. cross-term reduction, time–frequency resolution, angle or distance resolution) of SWD and WD for multicomponent linear frequency-modulated (LFM) signals processing is then observed by exploring the factor k selection results on two kinds of bi-component cases, including the one with a different frequency rate and the other one with the same frequency rate but having a different initial frequency. Correctness of the derived results and the SWD’s superiority in the instantaneous frequency estimation of noisy LFM signals compared with the WD are illustrated through simulations, and finally further discussions point out some promising future research directions and perspectives.

Harmonics Reduction for Resolver-to-Digital Conversion via Second-Order Generalized Integrator With Frequency-Locked Loop

Phase-locked loop (PLL) based resolver-to-digital conversion (RDC) can provide high-precision information of angular position and velocity for servo control system with resolver. However, there exist considerable harmonic components and random noises in the sinusoidal pair signals from resolver, which may impede further enhancement on the precision of RDC. In this paper, a signal filtering method is presented for RDC by combining two second-order generalized integrators (SOGIs) with a frequency-locked loop (FLL). In this method, FLL is designed in the form of second order to obtain high-accuracy estimate of resolver signal frequency, and two SOGIs are employed as frequency-adaptive band-pass filters to filter resolver pair signals by using the estimated frequency as the center frequency. Hence, the proposed method can track the fundamental components of resolver pair signals accurately, and thus harmonic components and noises can be reduced. Compared with the conventional SOGI-FLL, this method has better frequency adaptation and higher tracking accuracy since the accuracy of frequency estimation is improved by using second-order FLL. It resolves the problem of PLL in suppressing harmonics and low-frequency noises, thereby improving the accuracy of RDC. Simulation and experimental results demonstrate the effectiveness of the proposed method.

Precise Identification of Wideband Multiple Microwave Frequency Based on Self-Heterodyne Low-Coherence Interferometry

Frequency estimation of microwave signals is a crucial functionality for applications ranging from biomedical engineering to electronic warfare systems. Photonics-based frequency measurement systems offer advantages of flexible reconfigurability and wide bandwidth compard to electronic methods. However, photonic based systems are limited by trade-offs between measurement range and accuracy. Here, we propose and experimentally demonstrate a frequency identification system with ultrahigh accuracy of 900 kHz, large bandwidth of 39 GHz, and the capability of multiple frequencies estimation. The great performance is achieved by wideband distributed frequency-to-power mapping created by self-heterodyne low-coherence interferometry. The results show that the system we proposed is beneficial for applications in RF spectrum sensing of modern communication and radar applications.

Observer-based adaptive scheme for fixed-time frequency estimation of biased sinusoidal signals

In this technical communique, we propose a novel observer-based adaptive scheme to deal with the parameter estimation problem of biased sinusoidal signals. Different from the existing adaptive frequency estimation scheme, the proposed scheme can achieve fixed-time frequency estimation, whose convergence time is independent of the initial errors. Simulation example with different initial values shows the effectiveness of the theoretical result.

Design and Development of Adaptive filter for Real Time Signal Processing

In Communication the signal is distorted due to noise and the notch filters are used for eliminating unwanted frequencies For filtering the signal in a specific band Notch filter is used. Notch filter can pass the signal below and above notch frequency. In most of the signal processing applications frequency estimation of narrow band signals in noisy environment are required For frequency detection and tracking Adaptive IIR filter or Adaptive FIR filters can be used. Adaptive FIR Filter is more stable than Adaptive IIR filter. In most practical applications Adaptive IIR Notch Filter (AIIRNF)is used The advantage of Adaptive IIR notch filter over FIR Filter is less number of filter coefficients and less complexity in design In this paper Adaptive IIR Notch filter is designed for real time applications. The performance of designed adaptive IIR Notch filter is evaluated based on Magnitude and Frequency response.

Instantaneous frequency estimation for wheelset bearings weak fault signals using second-order synchrosqueezing S-transform with optimally weighted sliding window

The second-order synchrosqueezing S-transform (SSST2) is an important method for instantaneous frequency (IF) estimation of non-stationary signals. Based on the synchrosqueezing S-transform, the instantaneous frequency calculation method is modified using the second-order partial derivatives of time and frequency to achieve higher frequency resolution. However, weak multi-frequency signals with strong background noise are often drowned out during the transformation process. To achieve enhanced extraction of weak fault characteristic signals due to mechanical faults, this paper proposes an optimally weighted sliding window signal segmentation algorithm based on the SSST2. The results of simulations and experiments show that the time–frequency aggregation of the second-order synchrosqueezing S-transform based on the optimally weighted sliding window (OWSW-SSST2) is not only significantly higher than that of commonly used time–frequency transforms, but it also has better operational efficiency than the second-order synchrosqueezing S-transform. In this paper, the proposed algorithm is used to analyze fault signals from actual high-speed railway wheelset bearings. The results show that the OWSW-SSST2 algorithm greatly improves the spectral aggregation of the signal, and crucially, that high-precision IF estimates for signals can be obtained in low signal-to-noise ratio environments. This research is both of academic interest and significant for practical engineering use to ensure safe high-speed rail operations. It helps enable monitoring the status of wheelset bearings, correctly estimating the locations and causes of failures, and providing up-to-date systematic maintenance and system improvement strategies.

Cramér-Rao Bounds for spectral parametric estimation with compressive multiband architectures

This article tackles the topic of performance analysis for Spectrum Sensing based on Compressive Sampling (CS). More precisely, the lower bound on the variance of any unbiased estimator, the Cramér-Rao Bound (CRB), is investigated in the context of spectral parametric estimation. Compressed samples are obtained from a multiband architecture like the Modulated Wideband Converter, the Quadrature-Analog-to-Information Converter or the Periodic Non Uniform Sampler. An expression of the Fisher information matrix, which allows to compute the CRB, is established for a compressive multiband architecture assuming a disjoint spectral subband model. The relationships between Fisher matrices in a generic framework are exposed: first between compressive multiband and subsampling architectures, then between subsampling and Nyquist sampling architectures. Based on these new considerations, the issue of interferer detection, a canonical case and also a huge thorn in the side of wideband radiofrequency receivers is tackled. A benchmark between Nyquist, Subsampling and Compressive Multiband Sampling approaches is provided for frequency and amplitude estimation of dual-tone signals. This analysis illustrates the way in which interferences between parameters occur in estimation with Compressive Sampling. It is then shown how properties of the sensing matrix for popular compressive architectures enable to control the precision of spectral parametric estimation in specific subbands. This control opportunity opens the door to adaptive methods.

Cyclostationary Signals Analysis Methods Based on High-Dimensional Space Transformation Under Impulsive Noise

Cyclostationary signals analysis is a highly widespread tool for non-stationary signals processing. In practical transmission, signals may be contaminated by non-stationary non-Gaussian impulse noises. However, cyclostationary is weak in dealing with such non-Gaussian distributions. In this paper, a cyclic mean kernel function is proposed for cyclostationary signal analysis under impulse noise, based on a high-dimensional space transformation. Then, the generalized cyclic mean kernel function is proposed based on the constructed generalized Hankel matrix. The simulation results show that the cyclostationary signal frequency estimation methods based on these two functions have advantages in performance and robustness over the existing methods under impulsive noise.

Educational Simulator for Frequency Estimation using ANN

In this study, educational simulator for frequency estimation of signals is realized with artificial neural networks. Artificial neural networks are used for training Prony coefficients. Designed simulator is written in MATLAB and effect of neural net parameters (cost function, activation function, neuron size, etc.) to learning ability can be compared. Besides educational purposes, developed simulator can be used by engineers in order to create frequency estimators in practical studies.

Fine Doppler Frequency Estimation of Windowed Complex Sinusoidal Signals for Radar Systems

This article presents a new fine Doppler frequency estimation method of complex sinusoidal signals for radar systems. The proposed method can work with nonrectangular window functions to suppress the interference signal caused by the undesired spectral leakage. This method is based on an interpolation curve that uses the sum and difference of two discrete Fourier transform (DFT) magnitudes, and can estimate an accurate frequency between the interpolation curve samples through precise linear approximation. The proposed method exhibits lower computational complexity than the conventional method, which compensates the bias of an arbitrary window function and exhibits high performance. Thus, the proposed method is applicable to radar systems requiring fast processing time. Furthermore, the simulation results show that the proposed method outperforms the conventional method for various window functions.

Efficient interpolation based OMP for sparse channel estimation in underwater acoustic OFDM

To achieve higher accuracy of path delay estimation with lower computational complexity, the orthogonal matching pursuit (OMP) method with interpolation algorithm has been adopted for the sparse channel estimation, such as underwater acoustic (UWA) communication channels. For an orthogonal frequency division multiplexing (OFDM) system with uniform pilots, estimating the path delay by OMP in each its iteration is equivalent to the frequency estimation of single-tone signals with discrete Fourier transform (DFT). In this paper, based on the existing frequency estimation algorithms, we propose two novel interpolation based OMP methods for baseband sampling grid and over-sampling grid respectively, aiming at improving path delay estimation efficiency. Moreover, the closed-form of Cramer-Rao lower bound (CRLB) for single path delay estimation is derived to serve as a benchmark for simulations. The performances of the two proposed methods are verified by both simulations and UWA communication experiment in Yellow Sea, China, which show a higher estimation accuracy than that of the traditional OMP method, and the similar estimation performance but lower computational complexity than that of the existing high-accuracy interpolation based OMP method.

A robust and efficient instantaneous frequency estimator of multi-component signals with intersecting time-frequency signatures

An algorithm for multi-component instantaneous frequency (IF) estimation of signals with intersecting signatures in the time-frequency domain is proposed. The proposed algorithm exploits the slow variation in the IF and the direction of the IF curve to accurately track the IF without computing the complete time-frequency representation. The performance of the algorithm is illustrated using both synthetic and real-life signals. The proposed algorithm outperforms the state of art, such as Viterbi and adaptive directional time-frequency distribution based methods, in terms of the accuracy of IF estimates and computational complexity.

Multi-component instantaneous frequency estimation using signal decomposition and time-frequency filtering

A novel method is presented for the instantaneous frequency estimation of multi-component signals with crossing signatures in the time-frequency domain. The proposed method uses a combination of Eigen decomposition of time-frequency distributions and time-frequency filtering to recursively extract signal components from the original mixture and estimate their instantaneous frequencies. The proposed algorithm outperforms other algorithms of similar complexity in terms of mean square error accuracy.

Analysis of adaptive short-time Fourier transform-based synchrosqueezing transform

Recently, the study of modeling a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes has been a very active research area. The synchrosqueezing transform (SST) is a powerful method for instantaneous frequency estimation and component separation of non-stationary multicomponent signals. The short-time Fourier transform-based SST (FSST) reassigns the frequency variable to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. Very recently the FSST with a time-varying parameter, called the adaptive FSST, was introduced. The simulation experiments show that the adaptive FSST is very promising in instantaneous frequency estimation of the component of a multicomponent signal, and in accurate component recovery. However, the theoretical analysis of the adaptive FSST has not been carried out. In this paper, we study the theoretical analysis of the adaptive FSST and obtain the error bounds for the instantaneous frequency estimation and component recovery with the adaptive FSST and the second-order adaptive FSST.

Finer Granularity DFT Bins With Moving Window for Capacitance Sensing

In this article, the moving window discrete Fourier transform (MWDFT) with finer granularity bin indices is proposed for frequency estimation of periodic signals. The MWDFT structure is a cascade connection of comb filter and a complex resonator. The sign of comb filter is toggled between positive and negative using a multiplexer to select the integer and fractional bin indices. The sign of comb filter is chosen as negative for setting-up integer bin indices with certain resonator angle. The positive sign of comb filter rotates the zeros of the MWDFT to a specified angle in the anticlockwise direction in the z -plane. By selecting the positive feed forward coefficient, all odd harmonics of one-half of the fundamental frequency can be extracted from the MWDFT. This unique property of MWDFT with finer granularity bin indices is exploited to extract frequencies of finer resolution. A frequency locked loop is designed with MWDFT of finer granularity bins to estimate the frequency change of finer resolution. The proposed method is implemented on field programmable gate array (FPGA) as a capacitance measurement system. The method is able to provide better accuracy, wider frequency estimation range, and wider capacitance measurement range.