Multiple site electromyograph amplitude estimation

Temporal whitening of individual surface electromyograph (EMG) waveforms and spatial combination of multiple recording sites have separately been demonstrated to improve the performance of EMG amplitude estimation. This investigation combined these two techniques by first whitening, then combining the data from multiple EMG recording sites to form an EMG amplitude estimate. A phenomenological mathematical model of multiple sites of the surface EMG waveform, with analytic solution for an optimal amplitude estimate, is presented. Experimental surface EMG waveforms were then sampled from multiple sites during nonfatiguing, constant-force, isometric contractions of the biceps or triceps muscles, over the range of 10-75% maximum voluntary contraction. A signal-to-noise ratio (SNR) was computed from each amplitude estimate (deviations about the mean value of the estimate were considered as noise). Results showed that SNR performance: 1) increased with the number of EMG sites, 2) was a function of the sampling frequency, 3) was predominantly invariant to various methods of determining spatial uncorrelation filters, 4) was not sensitive to the intersite correlations of the electrode configuration investigated, and 5) was best at lower levels of contraction. A moving average root mean square estimator (245-ms window) provided an average ± standard deviation (A±SD) SNR of 10.7±3.3 for single site unwhitened recordings. Temporal whitening and four combined sites improved the A±SD SNR to 24.6±10.4. On one subject, eight whitened combined sites were achieved, providing an A±SD SNR of 35.0±13.4     

Single sideband quadrature amplitude modulation

Anew modulation scheme—single sideband quadrature amplitude modulation (SSB QAM) is proposed. This scheme allows to decrease the spectral width of the transferred signal by two times as opposed to the traditional quadrature amplitude modulation, while maintaining its spectral efficiency. This allows transmitting the modulated signal with the spectral width, which is equal to the spectral width of the modulating signal, and providing an energy gain of about 3 dB.     

Sequential amplitude estimation in multiuser communications

Considers the problem of multiuser amplitude estimation, i.e., the problem of estimating the amplitudes of several digital communications signals superimposed in the same channel. This problem is of importance in communications environments such as spread-spectrum radio networks, in which nonorthogonal multiplexing is used. Multiuser amplitude estimation is a critical prerequisite to the optimum demodulation of such signals using, for example, Verdu's algorithm. In the present paper, a sequential detection-estimation approach is applied to this problem, and several estimation paradigms, including the method of moments and likelihood-based estimators, are considered. The consistency, asymptotic variance, and complexity of these estimators are examined. A new method of constructing a recursive consistent and asymptotically efficient estimation algorithm out of a consistent estimator sequence is also suggested and is applied to the current setup. It is seen that detector-estimators that use these estimators in Verdu's algorithm result, asymptotically, in (known-amplitude) optimum error probabilities with little relative increase in complexity per demodulated bit     

Parameter estimation for random amplitude chirp signals

We consider the problem of estimating the parameters of a chirp signal observed in multiplicative noise, i.e., whose amplitude is randomly time-varying. Two methods for solving this problem are presented. First, an unstructured nonlinear least-squares approach (NLS) is proposed. It is shown that by minimizing the NLS criterion with respect to all samples of the time-varying amplitude, the problem reduces to a two-dimensional (2-D) maximization problem. A theoretical analysis of the NLS estimator is presented, and an expression for its asymptotic variance is derived. It is shown that the NLS estimator has a variance that is very close to the Cramer-Rao bound. The second approach combines the principles behind the high-order ambiguity function (HBF) and the NLS approach. It provides a computationally simpler but suboptimum estimator. A statistical analysis of the HAF-based estimator is also carried out, and closed-form expressions are derived for the asymptotic variance of the HAF estimators based on the data and on the squared data. Numerical examples attest to the validity of the theoretical analyzes and establish a comparison between the two proposed methods     

Electromyogram amplitude estimation with adaptive smoothing windowlength

Typical electromyogram (EMG) amplitude estimators use a fixed window length for smoothing the amplitude estimate. When the EMG amplitude is dynamic, previous research suggests that varying the smoothing length as a function of time may improve amplitude estimation. This paper develops optimal time-varying selection of the smoothing window length using a stochastic model of the EMG signal. Optimal selection is a function of the EMG amplitude and its derivatives. Simulation studies, in which EMG amplitude was changed randomly, found that the "best" adaptive filter performed as well as the "best" fixed-length filter. Experimental studies found the advantages of the adaptive processor to be situation dependent. Subjects used real-time EMG amplitude estimates to track a randomly-moving target. Perhaps due to task difficulty, no differences in adaptive versus fixed-length processors were observed when the target speed was fast. When the target speed was slow, the experimental results were consistent with the simulation predictions. When the target moved between two constant levels, the adaptive processor responded rapidly to the target level transitions and had low variance while the target dwelled on a level.     

Parameter estimation of 2-D random amplitude polynomial-phasesignals

Phase information has fundamental importance in many two-dimensional (2-D) signal processing problems. In this paper, we consider 2-D signals with random amplitude and a continuous deterministic phase. The signal is represented by a random amplitude polynomial phase model. A computationally efficient estimation algorithm for the signal parameters is presented. The algorithm is based on the properties of the mean phase differencing operator, which is introduced and analyzed. Assuming that the signal is observed in additive white Gaussian noise and that the amplitude field is Gaussian as well, we derive the Cramer-Rao lower bound (CRB) on the error variance in jointly estimating the model parameters. The performance of the algorithm in the presence of additive white Gaussian noise is illustrated by numerical examples and compared with the CRB     

Parameter estimation of an SSR amplitude comparison monopulse extractor

The letter summarises the results of an investigation on the monopulse receiver used in the ADSEL (selectively addressed secondary radar system). The results are the bias and the variance of the error as a function of the off-boresight angle and of the channels' mismatching.     

Adaptive whitening in electromyogram amplitude estimation for epoch-based applications

Epoch-based electromyogram (EMG) amplitude estimates have not incorporated signal whitening, even though whitening has demonstrated significant improvements for stream-based estimates. This paper presents new epoch-based algorithms, for both single- and multiple-channel EMG, which include a whitening stage. The best multiple-channel whitening processor provided a 21.4%-22.5% improvement over single-channel unwhitened estimation in an EMG-to-torque application.     

Adaptive whitening of the electromyogram to improve amplitude estimation

Previous research showed that whitening the surface electromyogram (EMG) can improve EMG amplitude estimation (where EMG amplitude is defined as the time-varying standard deviation of the EMG). However, conventional whitening via a linear filter seems to fail at low EMG amplitude levels, perhaps due to additive background noise in the measured EMG. This paper describes an adaptive whitening technique that overcomes this problem by cascading a nonadaptive whitening filter, an adaptive Wiener filter, and an adaptive gain correction. These stages can be calibrated from two, five second duration, constant-angle, constant-force contractions, one at a reference level [e.g., 50% maximum voluntary contraction (MVC)] and one at 0% MVC. In experimental studies, subjects used real-time EMG amplitude estimates to track a uniform-density, band-limited random target. With a 0.25-Hz bandwidth target, either adaptive whitening or multiple-channel processing reduced the tracking error roughly half-way to the error achieved using the dynamometer signal as the feedback. At the 1.00-Hz bandwidth, all of the EMG processors had errors equivalent to that of the dynamometer signal, reflecting that errors in this task were dominated by subjects' inability to track targets at this bandwidth. Increases in the additive noise level, smoothing window length, and tracking bandwidth diminish the advantages of whitening.     

Analytical formula for three points sinusoidal signals amplitude estimation errors

In this note, we show that the amplitude estimation of sinusoidal signals proposed in Wu and Hong [Wu, S.T., and Hong, J.L. (2010), ‘Five-point Amplitude Estimation of Sinusoidal Signals: With Application to LVDT Signal Conditioning’, IEEE Transactions on Instrumentation and Measurement, 59, 623–630] is a particular case of Vizireanu and Halunga [Vizireanu, D.N, and Halunga, S.V. (2011), ‘Single Sine Wave Parameters Estimation Method Based on Four Equally Spaced Samples’, International Journal of Electronics, 98(7), pp. 941–948]. An analytical formula for amplitude estimation errors as effects of sampling period deviation is obtained.     

Dictionary-based stochastic expectation-maximization for SAR amplitude probability density function estimation

In remotely sensed data analysis, a crucial problem is represented by the need to develop accurate models for the statistics of the pixel intensities. This paper deals with the problem of probability density function (pdf) estimation in the context of synthetic aperture radar (SAR) amplitude data analysis. Several theoretical and heuristic models for the pdfs of SAR data have been proposed in the literature, which have been proved to be effective for different land-cover typologies, thus making the choice of a single optimal parametric pdf a hard task, especially when dealing with heterogeneous SAR data. In this paper, an innovative estimation algorithm is described, which faces such a problem by adopting a finite mixture model for the amplitude pdf, with mixture components belonging to a given dictionary of SAR-specific pdfs. The proposed method automatically integrates the procedures of selection of the optimal model for each component, of parameter estimation, and of optimization of the number of components by combining the stochastic expectation-maximization iterative methodology with the recently developed "method-of-log-cumulants" for parametric pdf estimation in the case of nonnegative random variables. Experimental results on several real SAR images are reported, showing that the proposed method accurately models the statistics of SAR amplitude data.     

Single tone parameter estimation from discrete-time observations

Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed. The appropriate Cramér-Rao bounds and maximum-likelihood (MI.) estimation algorithms are derived. Some properties of the ML estimators are proved. The relationship of ML estimation to the discrete Fourier transform is exploited to obtain practical algorithms. The threshold effect of one algorithm is analyzed and compared to simulation results. Other simulation results verify other aspects of the analysis.     

Difference equation representation of chirp signals andinstantaneous frequency/amplitude estimation

We present a time-varying coefficient difference equation representation for sinusoidal signals with time-varying amplitudes and frequencies. We first obtain a recursive equation for a single chirp signal. Then, using this result, we obtain time-varying coefficient difference equation representations for signals composed of multiple chirp signals. We analyze these equations using the skew-shift operators. We show that the phases of the poles of the difference equations produce instantaneous frequencies (IF), and the magnitudes are proportional to the ratio of successive values of the instantaneous amplitudes (IA). Then algorithms are presented for the estimation of instantaneous frequencies and instantaneous amplitudes for multicomponent signals composed of chirps using the difference equation representation. The first algorithm we propose is based on the skew-shift operators. Next we derive the conditions under which we can use the so-called frozen-time approach. We propose an algorithm for IF and IA estimation based on the frozen-time approach. Then we propose an automatic signal separation method. Finally, we apply the proposed algorithms to single and multicomponent signals and compare the results with some existing methods     

Distributed multichannel speech enhancement with minimum mean-square error short-time spectral amplitude, log-spectral amplitude, and spectral phase estimation

In this paper, the authors present optimal multichannel frequency domain estimators for minimum mean-square error (MMSE) short-time spectral amplitude (STSA), log-spectral amplitude (LSA), and spectral phase estimation in a widely distributed microphone configuration. The estimators utilize Rayleigh and Gaussian statistical models for the speech prior and noise likelihood with a diffuse noise field for the surrounding environment. Based on the Signal-to-Noise Ratio (SNR) and Segmental Signal-to-Noise Ratio (SSNR) along with the Log-Likelihood Ratio (LLR) and Perceptual Evaluation of Speech Quality (PESQ) as objective metrics, the multichannel LSA estimator decreases background noise and speech distortion and increases speech quality compared to the baseline single channel STSA and LSA estimators, where the optimal multichannel spectral phase estimator serves as a significant quantity to the improvements, and demonstrates robustness due to time alignment and attenuation factor estimation. Overall, the optimal distributed microphone spectral estimators show strong results in noisy environments with application to many consumer, industrial, and military products.     

Precision of harmonic amplitude estimation on jitter corrupted data using sine fitting

The effect that jitter and phase noise have on the precision of amplitude estimation of the fundamental and harmonics of a periodic signal is studied. The analysis carried out is applicable to both Three-Parameter Sine Fitting as well as Coherent Discrete Fourier Transform procedures. An analytical expression for the standard deviation of estimated amplitude is presented. It shows that it is proportional to the jitter/phase noise standard deviation (for small amounts of jitter/phase noise) and inversely proportional to the square root of the number of data samples. The expression presented can be used to compute the estimation confidence intervals or determine the minimum number of samples that should be acquired in order to guarantee a given bound on the estimation precision.     

Complex amplitude estimation in the known steering matrix and generalized waveform case

We consider a special growth-curve (SGC) model with a known steering matrix and generalized waveform in the presence of unknown interference and noise. Several estimators of the complex amplitude based on this model are derived, including the methods of approximate maximum likelihood (AML), minimum variance distortionless response (MVDR), and amplitude and phase estimation (APES). We analyze the statistical properties of these estimators and show that in the presence of temporally white but spatially correlated noise and interference, AML is asymptotically statistically efficient for a large snapshot number while MVDR and APES are asymptotically equivalent but not statistically efficient. Via several numerical examples, we also show that when the noise and interference are both spatially and temporally correlated, the APES estimator can achieve better estimation accuracy and exhibit greater robustness than the other methods.     

SAR amplitude probability density function estimation based on a generalized Gaussian model.

In the context of remotely sensed data analysis, an important problem is the development of accurate models for the statistics of the pixel intensities. Focusing on synthetic aperture radar (SAR) data, this modeling process turns out to be a crucial task, for instance, for classification or for denoising purposes. In this paper, an innovative parametric estimation methodology for SAR amplitude data is proposed that adopts a generalized Gaussian (GG) model for the complex SAR backscattered signal. A closed-form expression for the corresponding amplitude probability density function (PDF) is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model. Specifically, the recently proposed "method-of-log-cumulants" (MoLC) is applied, which stems from the adoption of the Mellin transform (instead of the usual Fourier transform) in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant. For the developed GG-based amplitude model, the resulting MoLC estimates turn out to be numerically feasible and are also analytically proved to be consistent. The proposed parametric approach was validated by using several real ERS-1, XSAR, E-SAR, and NASA/JPL airborne SAR images, and the experimental results prove that the method models the amplitude PDF better than several previously proposed parametric models for backscattering phenomena.     

数字调幅广播系统中基于滑动窗口的二维信道估计

针对DRM数字广播系统,提出一种基于滑动窗口的二维信道估计方法.该方法首先对接收到的导频信号所在信道进行最小二乘估计,然后进行时间方向插值估计导频子载波上所有位置处的信道频率响应,最后通过一个滑动窗口在多径扩展域和多谱勒扩展域分别进行处理.对于快速时变信道,通过调整窗口的滑动步数,可以有效处理窗口内信道路径数和路径延迟可能变化的情况,从而显著降低了子载波间干扰和高斯白噪声的影响.理论分析和仿真表明,与现有信道估计相比,该方法具有估计精确、易于实现的优点.     

Quantum Bayes estimation of the amplitude of a coherent signal (Corresp.)

The complex amplitude of a coherent quantum signal in the presence of thermal noise is to be estimated when its real and imaginary parts have a Gaussian prior distribution. Cost functions of Gaussian, power-law, and delta-function forms are shown all to lead to the same optimum estimator.