Frequency estimation of a sinusoidal signal via a three-point interpolated DFT method with high image component interference rejection capability

This paper proposes a three-point Interpolated Discrete Fourier Transform (IpDFT) method for frequency estimation of a discrete-time sinusoidal signal. It is based on the maximum sidelobe decay (MSD) windows and is highly effective in rejecting the detrimental effect on the estimation accuracy due to the image component of the signal spectrum. This remarkable feature is achieved by using an analytical expression based on a suitable weighting of the three largest DFT spectrum samples. The proposed method provides good results when the effect of the spectral interference due to the image component dominates other estimation error sources. The accuracy of the proposed method and of other state-of-the-art methods such as the multi-point IpDFT methods and the four-parameter sine-fitting (4PSF) algorithm are compared through both computer simulations and experimental results in the case of ideal, noisy, and harmonically distorted sinusoids. A small number of acquired cycles is assumed in order to analyze situations in which the contribution from the image component interference is significant. The performed comparison shows that the proposed method outperforms the considered multi-point IpDFT methods when the Signal-to-Noise Ratio (SNR) is higher than 30 dB and the number of acquired cycles is enough small. The proposed method outperforms also the 4PSF algorithm when the frequency estimation error is dominated by harmonics rather than wideband noise.     

A Uniform White-Noise Model for Fixed-Point Roundoff Errors in Digital Systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.     

Evaluation of Fourier transform of impulse response of linear time invariant systems†

Evaluation of the Fourior transform of the system impulse response is an important aspect of the design of control systems. A method suggested hero requires only one cycle of sine or cosine wave to be applied as an input to the system. It is proved that the sum of the sampled values of the output response, at the sampling interval equal to the period of the input wave, directly yields the sign and cosine transforms respectively. The procedure is generalized to any number of complete cycles of input wave, as well as to n/2 cycles whore n is any odd positive integer.     

利用低位ADC获取高精度量化结果

模数变换中量化精度取决于ＡＤＣ的位数。对于固定模拟量，即使作多次量化值的平均，也不能提高精度。但在量化前使被量化信号叠加上一个噪声，作多次量化值的平均，则有可能提高量化精度。本文对此量化模型进行了严格、系统的数学分析，对叠加噪声采用正态分布和均匀分布这两种常见类型噪声的情况进行了详细的分析和比较。     

正弦波调制对谐振式陀螺中谐振信号的影响

谐振式光纤陀螺（R—FOG）是利用光学Sagnac效应实现对转动角速度检测的一种高精度惯性传感器件。理论分析了正弦波调制特性,搭建了光学微谐振腔的调制解调实验系统,实验对比了正弦波、锯齿波、三角波3种调制波形对谐振信号信噪比的影响,得出了正弦波调制效果最好,提高了谐振信号的信噪比。针对不同调制幅度和频率条件下的正弦波调制对谐振信号的影响进行了测试,得出了调制幅度和调制频率对谐振信号的影响,为光学微谐振腔在谐振式陀螺系统应用中相位调制选择最佳的参数提供了参考。     

随机信号雷达的发展

随机信号雷达是一种以微波噪声源作为其发射信号或信号调制形式的雷达,相对于传统的雷达体制,随机信号雷达具有许多优良的特性,本文介绍了过去３０多年中随机信号雷达的发展过程,对其基本形式和相关法,频谱法,反相关法等实现方法作出了系统的总结,并且对几种典型的随机信号雷达,如“随机调频连续波雷达”,“正弦加随机调频连;续波雷”和“随机二相码连续波雷达”的基本结构作了介绍,最后对随机号雷达的发展作了展望。     

基于核密度估计的故障诊断信号非均匀量化方法

在工业物联网的某些故障诊断场景中,由于缺少电信网络覆盖,采集信号通过远距离无线电（Long Range Radio,LoRa）技术实现无线可靠回传,但其较低的传输速率会限制故障诊断的精度。针对LoRa窄带宽的技术限制,提出了采样频率和量化分辨率固定条件下的时域信号非均匀量化方案。首先,通过建立基于核密度估计（Kernel Density Estimation,KDE）的非参数拟合模型,重点研究了带宽受限场景中合适的核函数类型和带宽确定准则,拟合生成传感信号幅度的概率密度函数（Probability Density Function,PDF）。其次,以PDF为输入,以最小化量化噪声为目标函数,通过非线性规划,输出最佳的一组非均匀量化电平值。其特点在于针对出现频次最高的时域幅度,采用更小的量化间隔,实现量化噪声的最小化。最后,以轴流风机状态检测为例进行了实验,结果表明,基座松动和轴承故障对量化电平的影响更大。随着量化分辨率的增加,KDE量化逐渐趋近均匀量化,相较于高斯量化的优势逐渐缩小。因此,提出的KDE量化方案适合窄带宽条件下的非均匀量化,可提高信道利用率,并在传输带宽和量化噪声之间取得折中。     

SENSORI-MOTOR PERFORMANCE UNDER VARYING NOISE CONDITIONS

A group of subjects performed a task in quiet and noisy environments. The noise was intermittent, within the frequency range of 75 to 9600 cycles and at sound levels of 70, 80, 90, and 100 db. The study was experimental, but simulated an occupational situation.

There was a tendency for more errors and less precision when working in the noisy environment. Response times were slower and the number of errors greater than when noise levels and frequencies were highest. The frequency range of 2400-4800 cycles was associated with the slowest response time and largest number of errors, both at 90 and 100 db.

It appears that intermittent noise may have a reducing effect on the individual's capacity for quick and precise execution of coordinated movements. The implications for safety and certain production tasks seem obvious.     

基于FPGA的高精度数字化正弦信号生成的新方法

提出了一种基于FPGA的高精度数字化正弦调制信号生成的新方法;该方法利用查表和线性插值相结合的办法,实时生成高精度正弦调制信号;首先介绍了新方法的基本原理及FPGA实现方案,然后对该方法进行了模型误差和量化误差分析,给出系统设计参考依据;最后,利用新方法产生500Hz的正弦调制信号对频率为13.552kHz三角载波进行调制生成SPWM波形,给出实验结果.     

Improving four-parameter sine wave fitting by normalization

Matrix equations need to be solved in each iterative round of four-parameter sine wave fitting. To ensure the robustness, normalizing factors rendering the minimum condition number (MCN) of the normal equation coefficient matrix was studied for the practical scenario (large sample size, and frequency well within [0, Nyquist Frequency]). Two parameter models, effective parameter model (EPM) and peak parameter model (PPM) were examined. The study shows that, firstly, with ignoring secondary entries of the coefficient matrix, the condition numbers depend solely on the amplitude of the four parameters. Secondly, for both models, there exists the optimal amplitude that renders the MCN. As amplitudes deviate from this optimal value, the condition number increases quickly. Thirdly, both the EPM and PPM possess a MCN close to 14. One numerical example shows that, if the realization data is normalized to the optimal amplitude, the condition numbers are indeed small, if the frequency lies in the practical range. With the initial frequency obtained from the method of the fast Fourier transform, outcomes at the fourth round iteration arrive to the Cramer–Rao bound.     

16 bit量化误差对正弦参数拟合影响的误差界

为了定量评估量化采样序列对四参数正弦拟合结果影响的误差规律,针对16 bit量化对四参数正弦拟合带来的影响,分别在有效位数、幅度、频率、初始相位和直流分量五项参数上进行了拟合误差界的搜索。选取的条件变量分别是幅度、序列所含波形的周波数、初始相位、直流分量以及序列数据点数。以两两联动的双条件组合方式进行误差界搜索,获得了各项参数的误差界随不同条件变化而变化的曲线规律,筛分出了显著影响量和不显著影响量,以及明确的误差上界和下界。以往的研究仅使用正态随机噪声方式表征其谐波失真以外的误差要素,本文揭示了量化误差影响的周期性特征,并以曲线包络方式给出了量化误差影响的误差界。量化误差对四参数拟合影响的误差界,可用于不确定度估计,以及测量条件选择。     

On the spectral factorization of nonstationary vector random processes

Conditions which depend on the covariance of a vector random process, sufficient to ensure the process can be generated by a linear, invertible system of finite order driven by white noise are derived, and equations which determine the parameters of the system are found. Some structural properties of lumped covariances are given; these stress the close relation between the structure of linear systems and that of lumped covariances and provide a means of establishing the minimal order of generating systems.     

非线性量化小脑模型关节控制器神经网络控制器

常规小脑模型关节控制器(CMAC)神经网络采用线性均匀量化,稳态控制精度与量化级数相关,增加量化级数可提高稳态精度但会导致内存空间和计算量的增加.本文提出一种可采用幂函数、高斯、分段3种非线性量化方法的非线性量CMAC神经网络,并分析了非线性量化CMAC的收敛性,解释了非线性量化提高稳态精度的本质.面向一阶惯性环节、二阶系统、一阶时变系统及二阶时变系统,分别跟踪方波、斜坡、正弦波、三角波和加速度等输入信号,仿真验证了非线性量化CMAC神经网络控制器的有效性,给出了不同非线性量化方法的适用性.结果表明,非线性量化CMAC参数容易设定,物理意义清晰,与常规CMAC对比,其快速性和控制精度显著提高,可以有效解决实际复杂非线性时变系统的控制.     

基于虚拟仪器的双通道语音数据采集系统

本文利用动态数据采集卡PCI-4451和图形化编程语言LabVIEW设计了一种基于虚拟仪器的双通道语音数据采集系统,该系统可以满足对动态语音信号进行高精度、高频率采样的要求,同时,可以对每个通道的动态输入范围进行单独设置,以保证量化噪声对动态范围不同的信号的影响尽可能保持一致.     

Direct estimation of noisy sinusoids using abductive networks

Spectral estimation techniques have been used for many years. In many cases, their complexity warrants investigating machine-learning alternatives where intensive computations are required only during training, with actual estimation simplified and speeded up. This allows using simple portable apparatus for fast and automated estimation in real time. We propose using abductive network machine learning for estimating both the amplitude and frequency of a single sine wave in the presence of additive Gaussian noise. Models synthesized by training on 1000 representative simulated sinusoids were evaluated on 500 new cases. With no phase variations and a signal to noise ratio of 7 dB, average absolute percentage errors for the sinusoid amplitude and period are 8.4% and 3.6%, respectively. Effects of the range of frequency variations and the noise level on the complexity and accuracy of the models were investigated. Amplitude and period estimates show signs of bias at a signal to noise ratio of 3 dB. Error variances track the Cramer-Rao bounds at high noise levels, with no thresholding observed down to 0 dB. The method is compared with a neural network model and with conventional discrete Fourier transform (DFT) based techniques and a Prony's based approach. The new approach is particularly useful when only a small portion of the sinusoid cycle is measured.     

Optimal Quantization of Signals for System Identification

In this technical note, we examine the optimal quantization of signals for system identification. We deal with memoryless quantization for the output signals and derive the optimal quantization schemes. The objective functions are the errors of least squares parameter estimation subject to a constraint on the number of subsections of the quantized signals or the expectation of the optimal code length for either high or low resolution. The optimal quantizer has the property that it is coarse near the origin of its output and becomes dense away from the origin in the usual situation. Finally the required quantity of data to decrease the total parameter estimation error, caused by quantization and noise, is discussed.      

网络控制系统动态量化H∞控制

基于线性矩阵不等式技术,采用状态反馈控制,考虑同时带有网络诱导随机丢包 和量化的H∞控制问题。考虑信号经网络从传感器到控制器和从控制器到执行器的传输中存在 通信诱导随机丢包,并采用动态量化器量化信号。设计H∞控制器的同时,提出量化的控制策 略,使得闭环系统在量化器的量化范围条件下指数均方稳定且具有指定的H∞性能指标。通过 数值仿真例子表明设计方法的有效性。     

直接数字频率合成中幅度量化误差分析

直接数字频率合成中，由于ＲＯＭ的数据位字长有限，因此存放在其中的正弦波幅值有量化误差，这个量化误差将在Ｄ／Ａ输出端产生杂散分量。本文把量化误差看作周期序列，对其在Ｄ／Ａ输出端产生的杂散分量平均功率进行了讨论，并分析了它的频谱特性。     

Speech authentication by semi-fragile speech watermarking utilizing analysis by synthesis and spectral distortion optimization

This paper proposes an improved semi-fragile speech watermarking scheme by quantization of linear prediction (LP) parameters, i.e., the inverse sine (IS) parameters. The spectral distortion due to watermark embedding is controlled to meet the ‘transparency’ criterion in speech coding. A modified bit allocation algorithm combined with watermarking is developed to determine the quantization step so that the ‘transparency’ requirement is satisfied. Due to the statistical nature, the LP coefficients estimated from the watermarked speech signal are different from the watermarked LP coefficients even in the absence of attacks. This effect is the cause of increase in decoding error and minimum authentication length. To tackle this problem, an Analysis by Synthesis (AbS) scheme is developed to reduce the difference between the estimated LP coefficients and the watermarked ones. The watermark detection threshold and minimum authentication length are then derived according to the probability of error and the signal to noise ratio (SNR) requirements. Experimental results show that the proposed AbS based method can effectively reduce the difference between the watermarked IS parameter and the extracted IS parameter when there is no attacks. In addition, the modified bit allocation algorithm can automatically find the appropriate quantization step used in the odd-even modulation so that the transparency requirement is satisfied.     

Performance analysis of stereo, vergence, and focus as depth cuesfor active vision

This paper compares the performances of the binocular cues of stereo and vergence, and the monocular cue of focus for range estimation using an active vision system. The performance of each cue is characterized in terms of sensitivity to errors in the imaging parameters. The effects of random, quantization errors are expressed in terms of the standard deviation of the resulting depth error. The effect of systematic, calibration errors on estimation using each cue is also studied. Performance characterization of each cue is utilized to evaluate the relative performance of the cues. Also discussed, based on such characterization, are ways to select a cue taking into account the computational and reliability aspects of the corresponding estimation process