Accurate spectral estimation based on measurements with adistorted-timebase digitizer

The timebase distortion present in an equivalent-time sampling oscilloscope introduces errors in the estimation of the values of the spectral components of a microwave signal when a classical discrete Fourier transform is used. A method is developed here to avoid these errors. The method is tested both in practice and with simulations. Two parts can be distinguished. At first, the timebase distortion is measured. This is done by digitizing a sinusoidal signal applied at the oscilloscope's input, and by calculating the phase of the analytical signal of the digitized waveform. Other possible methods to measure the timebase distortion are discussed, and it is shown why the method used is the most appropriate for our specific application. The knowledge of the timebase distortion is then used to build a least squares error estimator for the values of the spectral components of a digitized microwave signal. An experimental verification is done, from which is concluded that the method effectively removes the spectral estimation errors due to a timebase distortion     

Uncertainty of oscilloscope timebase distortion estimate

We study several problems related to the characterization of the timebase in high-speed sampling oscilloscopes. First, we examine the bias of using the method of the first-order approximation to estimate the additive and time jitter noises, and present a procedure to adjust for the bias in the estimates. We then study the bias and variance of a least-squares timebase distortion estimate that uses multiple sets of waveforms. Based on simulations, a method for calculating the uncertainty of the timebase distortion estimate is proposed. We also study the effects of amplitude and phase drifts, as well as jitter error on the estimation of timebase distortion. Results are shown using simulations with parameters that are closely related to those we observe in our laboratory     

正弦波拟合参数的不确定度评定

介绍了用4参数正弦波最小二乘拟合法拟合参数不确定度分析和评价过程。讨论了主要的不确定度来源,包括信号源误差、采集序列谐波失真、采集序列噪声及非谐波失真、采集序列中信号周期抖动、软件拟合运算误差的影响等,给出了减小不确定度的主要措施。结合一个幅度拟合实例给出了评价结果。     

交流增益的测量不确定度

介绍了用四参数正弦波最小二乘拟合法评价线性测量系统交流增益的不确定度分析和评价过程。讨论了主要的不确定度来源，包括信号源误差、采集序列的谐波失真、采集序列的噪声及非谐波失真、采集序列中信号周期的抖动、软件拟合运算误差的影响等等，给出了减小不确定度的主要措施。并结合一个实例，给出了评价结果。     

Phase-plane-derived distortion modeling of a fast and accurate digitizing sampler

Continued efforts to model the distortion behavior of custom-designed digitizing samplers for accurate measurement of dynamic signals are reported. This work is part of ongoing efforts at the National Institute of Standards and Technology (NIST) to advance the state of the art in waveform sampling metrology. In this paper, an analytic error model for a sampler having a -3-dB 6-GHz bandwidth is described. The model is derived from examination of the sampler's error behavior in the phase plane. The model takes as inputs the per-sample estimates of signal amplitude, first derivative, and second derivative, where the derivatives are with respect to time. The model's analytic form consists of polynomials in these terms, which are chosen from consideration of the voltage dependence of the digitizer input capacitance and the previously studied error behavior in a predecessor digitizer. At 1 GHz, an improvement in total harmonic distortion from -32 to -46 dB is obtained when model-generated sample corrections are applied to the waveform. The effect of timebase distortion in the sampling system is also accounted for and corrected. The inclusion of second-derivative dependence in the model is shown to improve the model's fit to the measured data by providing fine temporal adjustment of the fitted waveform.     

直流偏移的测量不确定度

介绍了用4参数正弦波最小二乘拟合法评价线性测量系统直流偏移指标时,测量不确定度分析和评价过程．通过使用国军标GJB 3756-1999“测量不确定度的表述及评定”中推荐的方法,讨论了影响评价结果不确定度的几个主要误差来源,包括信号源误差、采集序列的谐波失真、采集序列的噪声及非谐波失真、采集序列中信号周期的抖动、软件拟合运算误差的影响等,给出了直流偏移的测量不确定度及减小直流偏移指标评价不确定度的主要措施．在一个实际评价例子上,给出了直流偏移指标不确定度评价结果,表明该过程的正确性和切实可行性．该过程及结论可应用在对于计量标准进行直流偏移指标的不确定度分析上,也可用于估计直流偏移指标本身的不确定度．     

音频传输测试仪输出电平准确度校准

介绍一种使用有效值数字交流电压表、匹配电阻箱、频谱分析仪来校准音频传输测试仪输出电平准确度的方法,并给出了测量结果不确定度。经过对数百台音频传输测试仪的校准,证明方法可行。在缺乏相应仪器设备的前提下,利用实验室常用设备,实现了音频传输测试仪的校准。     

基于四参数正弦拟合的放大器延迟时间的精确测量

针对放大器延迟时间测量时信号幅度相差悬殊的问题,提出了四参数正弦拟合测量方式,以相位差转换成时间差予以实现。对其中的相位周期性带来粗大误差问题,负值幅度带来相位粗大误差问题,测量系统自身通道间延迟修正问题等,进行了分析讨论,并给出了解决方案。对测量结果的不确定度进行了分析。在实际应变放大器上的一组实验结果,验证了所述方法的有效性与可行性。并且发现,放大器的延迟具有内在稳定性,与激励信号的幅度、频率、波形等均无关系。该方法可用于放大器、滤波器、衰减器等线性电路延迟的测量分析。     

Time-base nonlinearity determination using iterated sine-fitanalysis

A new method is presented to determine the time-base errors of sampling instruments. The method does not require a time-base error model and thus provides accurate estimates where model-based methods fail. Measurements of sinewaves at multiple phases and frequencies are used as test signals. A harmonic distortion model is used to account for amplitude nonlinearity of the sampling channel. Use of an independent method for estimating the channel noise and jitter allows an accurate estimate of the harmonic order. Methods are presented for separating the harmonics generated by the sampling channel from those generated by the time-base distortion. The use of an iterative sine-fit procedure gives accurate results in a short time. A new weighting procedure is described, which minimizes the error in the estimates. Guidelines are given for selecting good sets of test frequencies. Results are shown for both simulated and real data     

Practical implementation of the phase-quantization technique in an iterative Fourier-transform algorithm

Implementation of the phase-quantization method in the design of computer-generated holograms (CGHs), especially binary CGHs, is a major influence on the diffraction efficiency of the CGHs. We describe the use of various quantization methods in the various steps of an iterative Fourier-transform algorithm and compare the root-mean-square (RMS) errors of the CGHs. As a result of the practical quantization technique, the most effective RMS value of a binary CGH should be decreased by at least 13% to retain maximum diffraction efficiency.     

Characterizing transient measurements by use of the step responseand the convolution integral

A method of determining the suitability of a divider system for making measurements of high-voltage transients is described. This method involves the convolution of the experimentally determined step response of the divider with various analytic waveforms which represent ideal waveforms expected in the experimental arrangement. The result of the convolution is compared, both graphically and in terms of relevant parameters such as peak amplitude and front time, with the original waveform. This procedure allows the distortion introduced by the convolution calculation to be seen clearly. The numerical implementation of the method is easily run on a personal computer     

残周期正弦波形参数拟合及其应用

介绍了残周期正弦波拟合问题的难点及解决思想:以无需初始值预估计的模型拟合方式,化解残周期波形时信息不够全面的问题,从而一举解决了残周期条件下的正弦波形最小二乘拟合问题。针对残周期条件下的正弦拟合的特殊性,介绍了正弦波局域失真的思想及概念,以及适应于局域波形的噪声信号比的概念,并给出了噪声信号比对于正弦参数拟合误差的影响规律。针对残周期正弦波拟合的应用,给出了几个典型的应用事例,包括超低频正弦参数的快速估计、AM和FM信号波形的数字化解调、冲击波形峰值的精确估计、其它正弦波拟合算法的初始值估计等。证明了方法的有效性、可行性和工程实用价值。     

A High-Resolution Error Plotter for Analog-to-Digital Converters

This paper describes an automatic error plotting system for analog-to-digital converters (ADC's) which measures the static errors of the device under test at every quantization band edge (QBE) and displays them in graphical form. A quantization band edge is defined as any ADC input voltage which produces two adjacent output codes, each with 50-percent probability. The error of the ADC is then defined as the difference between the actual and nominal values of a QBE. A feedback loop which seeks each QBE is central to the system. Sample plots show the ability of the system to display common types of ADC errors and to display error signatures that often point to specific ADC problems. Resolution, accuracy, and (to a large extent) speed of the system depend on the digital voltmeter chosen as a standard. In a typical case, a 2000 point plot can be made in two minutes with a resolution and accuracy exceeding the weight of the ADC's least significant bit by an order of magnitude.     

比较法相位型振动校准系统的研究和实现

介绍比较法振动传感器幅相特性测量技术的基本原理和传统实现方法。详细描述了一种新型的基于虚拟仪器技术的比较法相位型振动校准系统,它将绝对法振动校准中正弦逼近的算法运用于比较法,通过对参考传感器和被校传感器两路信号的采集和处理,能够在宽频带范围内实现加速度传感器复合灵敏度的精确校准,在小相位差的测量上实现了与相位标准同等级的精确测量。运用虚拟仪器技术,还能够实现信号频谱分析及失真度的精确计算。     

轴压荷载下钢管钢筋混凝土损伤状态超声检测研究

在轴压荷载下分别对素混凝土、钢筋混凝土、钢管混凝土和钢管钢筋混凝土的损伤状态进行超声检测,得到不同荷载下超声通过柱的中截面的波形图,定义波形图均方根振幅和均方根振幅比,并分析混凝土裂隙的变化过程。通过对波形图进行快速傅里叶变换得到频谱图,基于固体介质裂化吸收高频声波能量,使超声主频向低频移动的原理,应用频谱图的第一主频及其幅值变化分析钢管内混凝土和钢筋混凝土的损伤演变过程。结果表明:声波波形均方根振幅、均方根振幅比和第一主频及其幅值可以有效反映钢管内混凝土和钢筋混凝土的裂隙变化情况。轴压荷载作用下钢管内钢筋混凝土的损伤呈五段式变化,分别为核心混凝土裂缝产生并发展、混凝土在钢管约束作用下逐步密实、混凝土裂缝迅速扩展、钢管套箍作用加强段和钢管屈曲后构件丧失承载力。通过钢管外壁的应变分析,表明钢管对核心混凝土的约束作用阶段与超声检测判定的混凝土损伤演化过程一致。超声波技术可以准确检测轴压荷载作用下钢管内钢筋混凝土的损伤状态并确定钢管对混凝土套箍作用的发挥阶段。     

宽带取样示波器时基误差补偿的新方法研究

时基误差严重影响宽带取样示波器的高精准测量,但对时基误差进行精确估计和补偿极为困难。针对宽带取样示波器的时基误差(含时基失真与抖动引起的误差),首次运用正交距离回归算法对宽带取样示波器时基误差进行估计。对比多相位、多频率最小二乘法,该方法仅用一组近似正交的正弦信号对宽带取样示波器的时基误差进行有效估计,实现了对测量信号的时基补偿,得出了低于0.3ps的时基误差,显著提高了宽带取样示波器测量准确度。     

The use of DFT windows in signal-to-noise ratio and harmonicdistortion computations

The discrete Fourier transform (DFT) can be used to compute the signal-to-noise ratio (SNR) and harmonic distortion of a waveform recorder. When the data record contains a non-integer number of cycles of the sine wave, energy leaks from the sine wave and its harmonics to adjacent frequencies. A.L. Benetazzo et al. (1992) describe a windowed DFT method for computing the RMS value of a sine wave from the magnitude of the main lobe of its DFT and recommend the use of minimum energy windows. We present criteria for choosing the DFT window. A constraint for the window coefficients is derived to insure that quantization error does not influence the estimate of the amplitude of a sine wave from the main lobe of its DFT     

A comparison of ultrasonic wavefront distortion and compensation inone-dimensional and two-dimensional apertures

A comparison of wavefront distortion and compensation in one-dimensional and two-dimensional apertures is made using two-dimensional transmission measurements through 14 different specimens of human abdominal wall. The measurements were employed to emulate data in one dimension by summing waveforms in the elevation direction after a geometric correction was performed using a fourth-order polynomial fit to the surface of arrival time. Distortion calculation and time-shift compensation were performed independently on waveforms in the one-dimensional and two-dimensional apertures and the waveforms were focussed using a Fourier transform method to obtain the point-spread function in the central elevation plane. The results show that distortion is smoothed increasingly by one-dimensional apertures as the elevation dimension grows and that the smoothing is substantial for elevations similar to those employed in present clinical imagers. The results also show that one-dimensional compensation becomes less effective than two-dimensional compensation as the size of the elevation increases but that one-dimensional compensation performs almost as well as two-dimensional compensation in apertures with elevations like those in current imaging systems     

Effects of acoustic heterogeneity in breast thermoacoustic tomography

The effects of wavefront distortions induced by acoustic heterogeneities in breast thermoacoustic tomography (TAT) are studied. Amplitude distortions are shown to be insignificant for different scales of acoustic heterogeneities. For wavelength-scale, or smaller, heterogeneities, amplitude distortion of the wavefront is minor as a result of diffraction when the detectors are placed in the far field of the heterogeneities. For larger-scale heterogeneities at the parenchyma wall, by using a ray approach (geometric optics), we show that no refraction-induced multipath interference occurs and, consequently, that no severe amplitude distortion, such as is found in ultrasound tomography, exists. Next, we consider the effects of phase distortions (errors in time-of-flight) in our numerical studies. The numerical results on the spreads of point sources and boundaries caused by the phase distortions are in good agreement with the proposed formula. After that, we demonstrate that the blurring of images can be compensated for by using the distribution of acoustic velocity in the tissues in the reconstructions. The effects of the errors in the acoustical velocities on this compensation also are investigated. An approach to implement the compensation using only TAT data is proposed. Lastly, the differences in the effects of acoustic heterogeneity and the generation of speckles in breast TAT and breast ultrasound imaging are discussed.     

Error in calculating the amplitude spectrum of a polyharmonic signal from unequally spaced samples

This is an analytic study of errors in calculating the amplitude spectrum of a polyharmonic signal from a discrete sequence of samples that are unequally spaced owing to random deviations (jitter) in the sampling time. Relationships are derived between the aperture jitter and the errors in estimating the Fourier coefficients and the square of the amplitude and amplitude of a harmonic component, for uniform and normal (gaussian) probability distributions of these deviations.