Using sine wave histograms to estimate analog-to-digital converterdynamic error functions

This paper describes a new method for developing analog-to-digital converter (ADC) error function models using modified sinewave histogram methods. The error models may be used to digitally compensate for nonlinearities introduced by the converter. The histogram modification involves sorting of converter output samples based upon an estimated associated input derivative signal. This error model is based upon a previously unpublished result which shows that sinewave histograms yield distinctly different expected errors for each state based upon input signal slope associated with each output sample. This result thus provides a dynamic dependence for expected errors measured by means of histogram methods. Sorted sinewave histograms are used to estimate slope dependent expected errors at each ADC output state (code). The method provides improved error representation by providing error basis functions for every output code. Simulated results prove that this method removes all slope dependent errors for complex ADC architectures while experimental results for an 8-bit 200 MSPS ADC yielded more than 10 dB improvement in spurious-free-dynamic-range (SFDR) over the full Nyquist band. The new method is thus shown to possess wideband dynamic error character     

正弦波模型化测量方法及应用

本文对应用较多的几种正弦波模型化测量方法进行了综述,它们是曲线拟合法、直方图统计分析法、FFT法和拍频法。较详细地介绍了这几种测量方法的典型用途以及特点,通过比较几种方法的优缺点,讨论了它们应用中的局限性。     

Estimation of analogue-to-digital converter's signal-to-noise plus distortion ratio using the code histogram method

A procedure is proposed to estimate an analogue-to-digital converter's signal-to-noise plus distortion ratio using the histogram method. The procedure provides results that are in close agreement with the ones obtained with the spectral analysis and sinewave fitting methods. It is shown that the errors obtained by using former implementations of the histogram method are due to not considering the input stimulus probability density function, and it is shown how these errors can be rectified.     

Histogram Tests for Wideband Applications

Characterization and testing of analog-to-digital converters (ADCs) are important for many reasons. A histogram test is a common method to characterize the linearity features of an ADC. Two commonly used stimulus signals are sine waves and Gaussian noise. This paper presents a metrological comparison between Gaussian and sine-wave histogram tests for wideband applications, that is, we evaluate the performance of the characterization of the ADC and the usability of postcorrection. A postcorrection procedure involves the characterization of the ADC nonlinearity and then the use of this information by processing the ADC output samples to remove the distortion. The results show that the Gaussian histogram test gives reasonable accuracy in measuring nonlinearities. However, it does not result in a suitable model for postcorrection in wideband applications. A single-tone sine-wave histogram will be a better basis for postcorrection. The best result can be obtained if the lookup table is trained with several single-tone sine waves in the frequency band.     

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     

Moore响度的三种计算方法

简单介绍了Moore响度模型的计算过程,针对该模型以参数化方式输入信号频谱的特点,提出了直接FFT(快速傅里叶变换)频谱算法、FFT校正频谱算法和1/3倍频程谱算法等3条Moore响度计算路线,分析对比了3种不同算法对典型信号响度计算精度的影响。分析结果表明:对纯音或复合音信号,可采用FFT校正频谱算法或点数为4096的直接FFT频谱算法计算响度;对带宽较宽的噪声信号,建议采用1/3倍频程谱计算响度。     

INL reconstruction of A/D converters via parametric spectral estimation

The work presented in this paper builds on previous research done by the authors in detailing a novel procedure for obtaining a very fast measurement of the integral nonlinearity of an analog-to-digital converter (ADC). The core of the method is the parametric spectral estimation of the ADC output; the static characteristic is subsequently reconstructed as a sum of Chebyshev polynomials, in accordance with a previously developed procedure. The method allows one to test an ADC with sinusoids of any reasonable amplitude (even a slight overdrive is allowed), frequency (no synchronization is needed), and phase (which is digitally compensated). This approach is less accurate than the histogram test but incomparably faster (about 8000 samples are sufficient regardless of the ADC resolution).     

The extended function fast Fourier transform (EF-FFT)

The periodicity assumption implicit in fast Fourier transform (FFT) techniques can be utilized through time-domain prealiasing to obtain the spectral components of infinite-duration time-domain reflectometry signals when they can be modeled, outside the observation window, with step and/or exponential functions. The technique is shown to be more accurate than both conventional windowing and the other FFT approaches described in the literature for analysis of steplike signals. The duality equation relating the extension functions introduced in the extended function FFT (EF-FFT) method to conventional window functions is derived. Using this relation, it is shown that signals with high-frequency content only within the observation window are best analyzed with EF-FFT methods and that signals with time-distributed spectral components (e.g., speech) are best analyzed with conventional FFT methods     

ZFFT与Chirp-Z变换细化选带的频谱分析对比

在细化选带频谱分析中，复调制细化方法（ZFFT）和线性调频Z变换方法（Chirp—Z变换）是常用的两种方法。通过理论分析和仿真计算，对两者在算法、特点和误差方面进行对比分析表明：对于单频率和谱线干涉不严重的多频率谐波成分，使用FFT后进行校正，或者使用CZT细化分析，均能得到高精度的频率、幅值和相位，不必使用ZFFT；对于发生严重干涉现象的密集多频率谐波成分，ZFFT通过增大细化倍数后重采样，把干涉的各频率成分分离后进行校正可获得高精度的信号参数，但CZT只是把细化分析频带局部放大，无法消除干涉影响，提高频率分辨率也无法分离出信号的真实频率成分。通过增大采样点数，减少干涉产生的误差，CZT可以获得较高精度的信号参数，但却大大增加了运算时间。     

A new bidimensional histogram for the dynamic characterization of ADCs

A bidimensional histogram based on a dual-tone signal is proposed for testing analog-to-digital converters in the phase plane (output code, input signal slope). The bidimensional histogram of the actual code occurrences in the phase plane is compared with the ideal dual-tone probability distribution function in order to derive the actual transfer characteristic. With respect to the phase plane test via several single-tone acquisitions at different frequencies, the proposed histogram allows the phase plane coverage to be increased with the same sample number, the experimental burden to be reduced, and the metrological constraints of calibrators to be relaxed. Simulation and experimental results of characterization and validation highlight the effectiveness and the practical applicability in standardization of the proposed method.     

Discrete-time method for signal-to-noise power ratio measurement

The measurement of signal-to-noise power ratio (SNR) is of fundamental importance in many areas of electrical engineering, such as communications, signal processing, tests and measurements, circuits and systems, etc. In this paper, we propose two algorithms for estimating the signal-to-noise ratio of a noisy sinewave from discrete-time data obtained by sampling the input signal. One algorithm is based on the estimation of the four parameters of the input sinewave. The second algorithm is based on estimating the average noise power by averaging the squared magnitude of the FFT bins attributed to the noise. Both methods show excellent performance. Simulation results indicate that the four-parameter method requires the input SNR to be at least 10 dB and the input signal frequency not exceeding one-third of the sampling frequency. On the other hand, the second approach, the spectrum averaging method, shows a remarkable robustness over a very wide range of normalized frequencies (with respect to the Nyquist frequency) and SNRs (well over 100 dB). This spectrum averaging method should prove to be very useful in a wide range of applications     

ADC characterization based on singular value decomposition

A new method for ADC characterization, based on singular value decomposition, is introduced in this paper. Here, the singular values of the sampled data matrix, directly derived from the measured input data, are used to characterize the signal-to-noise ratio (SNR), and further to estimate the number of effective bits. Various input signals, such as single-tone, dual-tone, or multitone, can be used to obtain accurate estimation results. In addition, the new method avoids the difficulties and problems of the earlier characterization methods such as the sensitivity to the applied sinewave frequency and sampled data sizes, and the spectral leakage. Extensive simulations indicate that the proposed method provides excellent performance with single-tone, dual-tone, and multitone test signals. The proposed method also shows remarkable robustness over a truly wide SNR range: from 5 dB to 200 dB     

A Time-Domain Comparator Based Skipping-Window SAR ADC

This paper presents an energy efficient successive-approximation register (SAR) analog-to-digital converter (ADC) for low-power applications. To improve the overall energy-efficiency, a skipping-window technique is used to bypass corresponding conversion steps when the input falls in a window indicated by a time-domain comparator, which can provide not only the polarity of the input, but also the amount information of the input. The time-domain comparator, which is based on the edge pursing principle, consists of delay cells, two NAND gates, two D-flip-flop register-based phase detectors and a counter. The digital characteristic of the comparator makes the design more flexible, and the comparator can achieve noise and power optimization automatically by simply adjusting the delay cell number. An energy efficient digital-to-analog converter (DAC) control scheme suitable for the skipping window technique is also developed to reduce the switching energy during SAR conversion. Together with the skipping-window technique, the linearity and the power consumption of the SAR ADC are improved. The impact of different window sizes on comparison cycles, DAC switching energy and the overall energy efficiency is analyzed. Simulation results show that the proposed skipping-window technique can improve the overall energy-efficiency of the SAR ADC, as well as the linearity, and the optimized window size for the overall energy efficiency will vary with the DAC switching energy.     

Bounds on least-squares four-parameter sine-fit errors due toharmonic distortion and noise

Least-squares sine-fit algorithms are used extensively in signal-processing applications. The parameter estimates produced by such algorithms are subject to both random and systematic errors when the record of input samples consists of a fundamental sine wave corrupted by harmonic distortion or noise. The errors occur because, in general, such sine-fits will incorporate a portion of the harmonic distortion or noise into their estimate of the fundamental. Bounds are developed for these errors for least-squares four-parameter (amplitude, frequency, phase, and offset) sine-fit algorithms. The errors are functions of the number of periods in the record, the number of samples in the record, the harmonic order, and fundamental and harmonic amplitudes and phases. The bounds do not apply to cases in which harmonic components become aliased     

基于全相位FFT的油套环空中声速计算方法

油套环空中会产生各种噪声,使测得的接箍反射信号非常复杂,环隙中真实的声速则很难计算准确,可通过对原始接箍数据进行傅里叶变换的方法对声速进行估计,但是存在不可忽视的误差。全相位傅里叶变换是傅里叶变换的一种改进方法,能够获得更加准确的频率谱与相位谱。文章采用全相位快速傅里叶变换（all-phase Fast Fourier Transform,apFFT）得到原始接箍信号的频谱,然后通过该频谱进一步计算环隙声速,可得到更加准确的声速估计。通过对不同信噪比下的模拟接箍信号采用快速傅里叶变换（Fast Fourier Transform,FFT）和全相位快速傅里叶变换（apFFT）得到其频谱,可以验证apFFT具有很强的抑制频谱泄漏的能力,且抗噪性能比FFT更好。根据FFT谱和apFFT谱分别计算出声速并对比其精度,可以验证通过apFFT谱计算出的声速稳定性更好、精度更高。然后采用上述两种方法对不同深度井的实测接箍数据进行频谱分析与对比,验证了apFFT较之于FFT对谱峰位置的辨识能力更强,根据谱峰位置计算声速的准确性也将更高。     

Measuring Thin Transparent Films Precisely

Fast Fourier transform (FTT) and nonlinear regression analysis are established analysis methods in the context of reflectometric layer thickness determination on thin transparent films. Where applicable, FFT is a very fast method for determining film thickness, but with limitations in resolution. The far more complex nonlinear regression analysis provides more accurate results. But it also has its problems which are discussed here.     

采样序列长度及周波数对正弦参数拟合的影响

针对波形拟合法估计正弦参数时,测量条件对拟合参数带来的误差影响,进行了拟合误差界的搜索研究。选取的条件变量分别是A/D位数、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,获得了幅度、频率、相位、直流分量、动态有效位数等拟合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。并对A/D位数、序列所含波形的周波数、以及序列数据点数带来的影响进行了深入研究,获得了拟合参数的误差界呈现量子化阶梯特征的显著规律,并获得了量子化阶梯边界点估计的经验公式。该结果可用于拟合正弦参数的误差评价和不确定度估计,也可以用于在设定拟合误差和不确定度情况下,选择测量条件。     

Testing of Precision DAC Using Low-Resolution ADC With Wobbling

Testing of high-resolution, digital-to-analog converters (DACs) with gigahertz clock rates is a challenging problem. The bottleneck is fast and accurate output measurement. This paper presents a novel high-performance DAC testing approach that uses a flash analog-to-digital converter (ADC) to achieve highspeed data acquisition, adopts the wobbling technique to provide a sufficient resolution, and processes the data with a sophisticated algorithm to guarantee high test accuracy. Simulation results show that, by using a 6-bit ADC and wobbling, the static linearity of 14-bit DACs can be tested to better than 1-LSB accuracy. The experimental results that are included in the paper also affirm the performance of the algorithm. This method provides a solution to both the production and on-chip testing problems of high-performance DACs.     

基于Matlab的ADC自动测试系统开发

阐述了模数转换器的静态参数和动态参数测试原理和方法,并且构建了模数转换器的自动测试硬件平台和软件系统.重点讨论了利用Matlab库函数进行快速傅立叶变换测试的方法,使用ADC自动测试系统对高速模数转换器SCM530101进行了测试,并给出了测试结果.     

Using Radial-basis Function Network for CLV

Analysis and comparing with three existing and popularly used forcasting customer lifetime value(CLV) methods,which are the Dwyer method,customer event-method and fitting method,and using performances of the existent artificial neural network,we apply the Radial-basis Function (RBF) network to forecast the CLV,the RBF network can approach the objective function partially.To every input/output pairs,it only needs adjust the weight a little and learn quickly which is very important to the forecast precision.Simulation and experimental results on the customers‘ data of a company in Shaanxi Province reveal the effectiveness and feasibility of the RBF network.