基于级联自适应陷波器的正弦波频率估计

常用的传统和现代方法对于噪声环境中正弦信号的频率估计均存在一定的缺陷。本文利用二阶陷波器级联构造自适应陷波器,实现对多个信号频率的估计;采用递推误差信号和递推最小二乘法同时优化各个二阶陷波器的参数。仿真结果表明,该方法对于单频、多频和频率变化等情况均具有较好的估计结果,且对于噪声干扰具有较强的鲁棒性。     

Estimation of the Parameters of Sinusoidal Signals in Non-Gaussian Noise

Accurate estimation of the amplitude and frequency parameters of sinusoidal signals from noisy observations is an important problem in many signal processing applications. In this paper, the problem is investigated under the assumption of non-Gaussian noise in general and Laplace noise in particular. It is proven mathematically that the maximum likelihood estimator derived under the condition of Laplace white noise is able to attain an asymptotic Cramer-Rao lower bound which is one half of that achieved by periodogram maximization and nonlinear least squares. It is also proven that when applied to non-Laplace situations, the Laplace maximum likelihood estimator, which may also be referred to as the nonlinear least-absolute-deviations estimator, can achieve an even higher statistical efficiency especially when the noise distribution has heavy tails. A computational procedure is proposed to overcome the difficulty of local extrema in the likelihood function. Simulation results are provided to validate the analytical findings.     

Robust estimation of a single complex sinusoid in whitenoise-H∞ filtering approach

A novel robust estimator is proposed for extracting a single complex sinusoid and its parameter (frequency) from measurements corrupted by white noise. This estimator is called an H_∞ sinusoidal estimator (HSE), which is derived by applying an H_∞ filter to a noisy sinusoidal model with the state-space representation. Simulations demonstrate that the HSE is more robust to the nature of observation noise {v_k} than the Kalman sinusoidal estimator (KSE), which is an improved version of the nonlinear filter previously proposed by the author     

一种新的自适应语音增强系统

针对自适应噪声对消(ANC)语音增强系统的性能高度依赖于参考信号的质量，任何原始语音信号泄漏到参考信号中，都会导致原始语音信号失真和噪声抵消性能恶化这一问题，本文提出一种对泄漏不敏感的附加随机噪声(ARN)自适应噪声对消语音增强系统。它通过在参考信号中加入一个低功率的宽带随机训练信号，然后用该训练信号作参考信号对噪声传输函数(NTF)进行自适应建模，并在使用自适应预测滤波器(APF)消除NTF自适应建模的语音信号干扰的同时，用补偿滤波器(CPF)来修正由APF引起的参考信号失真。计算机仿真表明，这种ARNANC语音增强系统在泄漏情况下能将原始语音信号从带噪语音信号中有效分离出来。     

A complex adaptive notch filter using modified gradient algorithm

A modified gradient algorithm is developed for improving the convergence speed of a first-order complex adaptive IIR notch filter, which is used for estimating an unknown frequency of a complex sinusoidal signal embedded in white Gaussian noise. The new cost function using new error criterion is presented and analyzed theoretically. The proposed technique can significantly improve the convergence speed as compared with a complex notch filter using plain gradient algorithm. The computer simulations are conducted to demonstrate the validity of the proposed complex adaptive notch filter.     

A Bayesian estimation approach for speech enhancement using hiddenMarkov models

A Bayesian estimation approach for enhancing speech signals which have been degraded by statistically independent additive noise is motivated and developed. In particular, minimum mean square error (MMSE) and maximum a posteriori (MAP) signal estimators are developed using hidden Markov models (HMMs) for the clean signal and the noise process. It is shown that the MMSE estimator comprises a weighted sum of conditional mean estimators for the composite states of the noisy signal, where the weights equal the posterior probabilities of the composite states given the noisy signal. The estimation of several spectral functionals of the clean signal such as the sample spectrum and the complex exponential of the phase is also considered. A gain-adapted MAP estimator is developed using the expectation-maximization algorithm. The theoretical performance of the MMSE estimator is discussed, and convergence of the MAP estimator is proved. Both the MMSE and MAP estimators are tested in enhancing speech signals degraded by white Gaussian noise at input signal-to-noise ratios of from 5 to 20 dB     

A nonlinear filter for estimating a sinusoidal signal and itsparameters in white noise: on the case of a single sinusoid

A nonlinear filter is proposed for estimating a complex sinusoidal signal and its parameters (frequency, amplitude, and phase) from measurements corrupted by white noise. This filter is derived by applying an extended complex Kalman filter (ECKF) to a nonlinear stochastic system whose state variables are a function of its frequency and a sample of an original signal, and then, proof of the stability is given in the case of a single complex sinusoid. Simulations demonstrate that the proposed nonlinear filter is effective as a method for estimating a single complex sinusoid and its frequency under a low signal-to-noise ratio (SNR). In addition, the effect of the initial condition in the filter on frequency estimation is also discussed     

A Novel Technique for the Identification of ARMA Systems Under Very Low Levels of SNR

In this paper, a novel technique for the identification of minimum-phase autoregressive moving average (ARMA) systems from the output observations in the presence of heavy noise is presented. First, starting from the conventional correlation estimator, a simple and accurate ARMA correlation (ARMAC) model in terms of the poles of the ARMA system is presented in a unified manner for white noise and impulse-train excitations. The AR parameters of the ARMA system are then obtained from the noisy observations by developing and using a residue-based least-squares correlation-fitting optimization technique that employs the proposed ARMAC model. As for the estimation of the MA parameters, it is preceded by the application of a new technique intended to reduce the noise present in the residual signal that is obtained by filtering the noisy ARMA signal via the estimated AR parameters. A scheme is then devised whereby the task of MA parameter estimation is transformed into a problem of correlation-fitting of the inverse autocorrelation function corresponding to the noise-compensated residual signal. In order to demonstrate the effectiveness of the proposed method, extensive simulations are performed by considering synthetic ARMA systems of different orders in the presence of additive white noise and the results are compared with those of some of the existing methods. It is shown that the proposed method is capable of estimating the ARMA parameters accurately and consistently with guaranteed stability for signal-to-noise ratio (SNR) levels as low as $-{5}~{hbox {dB}}$ . Simulation results are also provided for the identification of a human vocal-tract system using natural speech signals showing a superior performance of the proposed technique in terms of the power spectral density of the synthesized speech signal.      

Adaptive subsample delay estimation using a modified quadrature phase detector

An online delay estimation algorithm based upon an analogue quadrature phase detector that is suitable for determining the subsample delay between two noisy sinusoidal signals is introduced. The new technique is based on the recently proposed discrete-time quadrature-delay estimator (QDE). The algorithm uses the in-phase and quadrature-phase components of the received signals to produce a bias-free estimate of the delay between the input signals. The technique directly minimizes the delay error estimate, which is in turn used to adapt the coefficients of a simple fractional-delay filter (FDF). The algorithm is insensitive to variations in the amplitudes of the input signals, and does not require an accurate prior estimate of the frequency of the input sinusoids. The algorithm directly updates the delay error estimate, which is in turn used directly as the coefficient input to an adaptive FDF. The technique is simple to implement and has a reduced complexity compared to other adaptive techniques. Simulations show that in the presence of system noise, the new estimator outperforms conventional FDF-based estimators.     

Robust state estimator design for a solar battery charging system

This article describes a robust state estimator design for a solar battery charger where there is significant noise in the output measurements of the solar array voltage that causes degradation in the performance of the maximum power point tracking. The application of the extended Kalman filter, to the photovoltaic system, can lead to enhanced state estimation results so that a recursive solution can be obtained to achieve the most accurate estimate from the noisy signals. Additionally, as a consequence of applying the Kalman filter (KF), the immeasurable state of the inductor current can be estimated without a current sensor. The proposed controller uses the estimated solar array voltage for maximum power point tracker, and the estimated inductor current for determining the battery current controller. The methods for system modeling and design of the extended KF are presented, and the experimental results verify the validity of the proposed system.     

Multirate modeling of AR/MA stochastic signals and its applicationto the combined estimation-interpolation problem

The use of the Kalman filter is investigated in this work for interpolating and estimating values of an AR or MA stochastic signal when only a noisy, down-sampled version of the signal can be measured. A multirate modeling theory of the AR/MA stochastic signals is first derived from a block state-space viewpoint. The missing samples are embedded in the state vector so that missing signal reconstruction problem becomes a state estimation scheme. Next, Kalman state estimation theory is introduced to treat the combined estimation-interpolation problem. Some extensions are also discussed for variations of the original basic problem. The proposed Kalman reconstruction filter can be also applied toward recovering missing speech packets in a packet switching network with packet interleaving configuration. By analysis of state estimation theory, the proposed Kalman reconstruction filters produce minimum-variance estimates of the original signals. Simulation results indicate that the multirate Kalman reconstruction filters possess better estimation/interpolation performances than a Wiener reconstruction filter under adequate numerical complexity     

SVD analysis by synthesis of harmonic signals

An analysis by synthesis procedure based on the singular value decomposition (SVD) methodology is proposed. Using this procedure, a criterion for detecting the number of sinusoidal signals in the presence of noise is defined. Consecutive reconstructions are performed, and the resulting error power is compared to the noise variance in order to get the best approximation of the original noncorrupted signal. The number of the singular values corresponding to a reconstruction error power as close as possible to the noise variance gives the parsimonious order. The existence of such a criterion is important for both high-quality reconstruction and spectral analysis. Various spectral estimation techniques used on a reconstructed signal make it possible to retrieve harmonics in a highly noisy environment with very short data lengths     

Parameter estimation of exponentially damped sinusoids using ahigher order correlation-based approach

A very common problem in signal processing is parameter estimation of exponentially damped sinusoids from a finite subset of noisy observations. When the signal is contaminated with colored noise of unknown power spectral density, a cumulant-based approach provides an appropriate solution to this problem. We propose a new class of estimator, namely, a covariance-type estimator, which reduces the deterministic errors associated with imperfect estimation of higher order correlations from finite-data length. This estimator allows a higher order correlation sequence to be modeled as a damped exponential model in certain slices of the moments plane. This result shows a useful link with well-known linear-prediction-based methods, such as the minimum-norm principal-eigenvector method of Kumaresan and Tufts (1982), which can be subsequently applied to extracting frequencies and damping coefficients from the 1-D correlation sequence. This paper discusses the slices allowed in the moments plane, the uses and limitations of this estimator using multiple realizations, and a single record in a noisy environment. Monte Carlo simulations applied to standard examples are also performed, and the results are compared with the KT method and the standard biased-estimator-based approach. The comparison shows the effectiveness of the proposed estimator in terms of bias and mean-square error when the signals are contaminated with additive Gaussian noise and a single data record with short data length is available     

Minimax estimation of unknown deterministic signals in colorednoise

The estimation of a deterministic signal corrupted by random noise is considered. The strategy is to find a linear noncausal estimator which minimizes the maximum mean square error over an a priori set of signals. This signal set is specified in terms of frequency/energy constraints via the discrete Fourier transform. Exact filter expressions are given for the case of additive white noise. For the case of additive colored noise possessing a continuous power spectral density, a suboptimal filter is derived whose asymptotic performance is optimal. Asymptotic expressions for the minimax estimator error are developed for both cases. The minimax filter is applied to random data and is shown to solve asymptotically a certain worst-case Wiener filter problem     

Semiparametric estimation of the frequency of unknown periodic functions and its application to laser vibrometry signals

We propose a semiparametric approach to fundamental frequency estimation of an unknown periodic signal in additive white noise based on model selection. Our estimator maximizes a penalized version of the cumulated periodogram and is proved to be consistent and asymptotically efficient under very general conditions. When the number of observations is fixed, an implementation of this estimation method is proposed and illustrated on specific synthetic signals which arise in laser vibrometry. We extend this method for estimating the fundamental frequencies of two periodic functions having different fundamental frequencies when the data consist of their sum and additive white noise. We also compare the performances of our procedure with the so-called microdoppler technique, which is commonly used for laser vibrometry signals analysis. We show on simulated data that the penalized cumulated periodogram yields an accurate estimation of the frequencies at very low signal-to-noise ratios.     

Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses

Based on the linear prediction property of sinusoidal signals, two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed. In order to achieve accurate frequency estimation, the first algorithm uses a generalized unit-norm constraint, while the second method employs a monic constraint. The weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner. For the case of a single real tone with sufficiently large data samples, both estimators provide nearly identical frequency estimates and their performance approaches Crame/spl acute/r-Rao lower bound (CRLB) for white Gaussian noise before the threshold effect occurs. Algorithms for closed-form single-tone frequency estimation are also devised. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the CRLB for different frequencies, observation lengths and signal-to-noise ratio (SNR) conditions.     

稳定分布噪声下基于Merid滤波的跳频信号参数估计

常规时频分析方法是处理跳频(FH)信号的有力工具,但在稳定分布噪声环境下无法有效地实现参数估计。该文提出基于Merid滤波的时频分析方法对跳频信号进行参数估计。Merid滤波器可以有效地抑制稳定分布噪声,该文先对观测信号进行Merid滤波,再采用短时傅里叶变换(STFT)进行参数估计。仿真结果表明,在稳定分布噪声环境中,该方法的跳频信号参数估计性能优于基于分数低阶和基于Myriad滤波的两种时频分析方法。     

一种非均匀采样下小信号的检测方法

非均匀采样由于其具有不受采样频率限制、频率分辨率高以及抗混叠等优点,使得其应用十分广泛。但非均匀采样会引起信号的频谱噪声,这样使得非均匀采样下小信号的检测不易实现。本文分析了非均匀采样引起频谱噪声的原因,提出一种基于非均匀采样的小信号检测方法。该方法根据非均匀采样检测得到的大幅度信号,应用陷波器将其消除,降低了由大信号引起的频谱噪声,从而检测出小信号。文中详细说明了陷波方法的原理、陷波器宽度和深度的选择、陷波器中心频率的确定以及陷波器在非均匀采样下的应用,最后给出实验结果。理论和实验表明,基于非均匀采样的陷波方法是一种行之有效的信号频率检测方法,使用该方法处理信号可以得到准确的频率估计效果,检测出信号幅度相差100倍以上的多个信号频率。     

An adaptive estimation of periodic signals using a Fourier linearcombiner

Presents an adaptive algorithm for estimating from noisy observations, periodic signals of known period subject to transient disturbances. The estimator is based on the LMS algorithm and works by tracking the Fourier coefficients of the data. The estimator is analyzed for convergence, noise misadjustment and lag misadjustment for signals with both time invariant and time variant parameters. The analysis is greatly facilitated by a change of variable that results in a time invariant difference equation. At sufficiently small values of the LMS step size, the system is shown to exhibit decoupling with each Fourier component converging independently and uniformly. Detection of rapid transients in data with low signal to noise ratio can be improved by using larger step sizes for more prominent components of the estimated signal. An application of the Fourier estimator to estimation of brain evoked responses is included     

Current control strategy for power conditioners using sinusoidal signal integrators in synchronous reference frame

In this paper, a current control scheme, based on proportional-integral regulators using sinusoidal signal integrators (SSIs), is proposed for shunt type power conditioners. The aim is to simplify the implementation of SSI-based current harmonic compensation for industrial implementations where strict limitations on the harmonic distortion of the mains' currents are required. To compensate current harmonics, the SSIs are implemented to operate both on positive and negative sequence signals. One regulator, for the fundamental current component, is implemented in the stationary reference frame. The other regulators, for the current harmonics, are all implemented in a synchronous reference frame rotating at the fundamental frequency. This allows the simultaneous compensation of two current harmonics with just one regulator, yielding a significant reduction of the computational effort compared with other current control methods employing sinusoidal signal integrators implemented in stationary reference frame. A simple and robust voltage filter is also proposed by the authors to obtain a smooth and accurate position estimation of the voltage vector at the point of common coupling (PCC) under distorted mains' voltages. The whole control algorithm has been implemented on a 16-b, fixed-point digital signal processor (DSP) platform controlling a 20-kVA power conditioner prototype. The experimental results presented in this paper for inductive and capacitive loads show the validity of the proposed solutions.