Accurate spectral test algorithms with relaxed instrumentation requirements

Spectral testing is widely used to test the dynamic linearity performance of Analog-to-Digital Converters (ADC) and waveform generators. Dynamic specifications for ADCs are very important in high speed applications such as digital communications, ultrasound imaging and instrumentation. With improvements in the performance of ADCs, it is becoming an expensive and challenging task to perform spectral testing using standard methods due to the requirement that the test instrumentation environment must satisfy several stringent conditions. In order to address these challenges and to decrease the test cost, in this dissertation, three new algorithms are proposed to perform accurate spectral testing of ADCs by relaxing three necessary conditions required for standard spectral testing methods. The testing is done using uniformly sampled points. The first method introduces a new fundamental identification and replacement (FIRE) method, which eliminates the requirement of coherent sampling when using the DFT for testing the spectral response of an ADC. The robustness and accuracy of the proposed FIRE method is verified using simulation and measurement results obtained with non-coherently sampled data. The second method, namely, the Fundamental Estimation, Removal and Residue Interpolation (FERARI) method, is proposed to eliminate the requirement of precise control over amplitude and frequency of the input signal to the ADC. This method can be used when the ADC output is both non-coherently sampled and clipped. Simulation and measurement results using the FERARI method with non-coherently sampled and clipped outputs of the ADC are used to validate this approach. A third spectral test method is proposed that simultaneously relaxes the conditions of using a spectrally pure input source and coherent sampling. Using this method, the spectral characteristics of a high resolution ADC can be accurately tested using a non-coherently sampled output obtained with a sinusoidal input signal that has significant and unknown levels of nonlinear distortion. Simulation results are presented that show the accuracy and robustness of the proposed method. Finally, the issue of metastability in comparators and Successive Approximation Register (SAR) ADCs is analyzed. The analysis of probability of metastability in SAR ADCs with and without using metastable detection circuits is provided. Using this analysis, it is shown that as the frequency of sampling clock increases, using a metastable detection circuit decreases the probability of metastability in SAR ADC

Spectral Test via Discrete Tchebichef Transform for Randomness

Random key plays essential roles in cryptography. NIST statistical test suite for randomness is the most comprehensive set of random tests. It has been popular and used as a benchmark test for randomness. One of the random tests is spectral test. There has been some serious problem in spectral test as pointed out by few researchers. In this paper, an alternative test shall be proposed to replace the spectral test. The distribution of discrete orthonormal Tchebichef transform has been obtained based on computational observation being made on random noise. A recommendation on the new random test setting for short cryptographic keys shall also be made

Time-varying return predictability in the Chinese stock market

China's stock market is the largest emerging market all over the world. It is widely accepted that the Chinese stock market is far from efficiency and it possesses possible linear and nonlinear dependence. We study the predictability of returns in the Chinese stock market by employing the wild bootstrap automatic variance ratio test and the generalized spectral test. We find that the return predictability vary over time and significant return predictability is observed around market turmoils. Our findings are consistent with the Adaptive Markets Hypothesis and have practical implications for market participants.Comment: 11 Latex pages including 2 figures and 1 tabl

A bootstrapped spectral test for adequacy in weak ARMA models

This paper proposes a Cramér-von Mises (CM) test statistic to check the adequacy of weak ARMA models. Without posing a martingale difference assumption on the error terms, the asymptotic null distribution of the CM test is obtained. Moreover, this CM test is consistent, and has nontrivial power against the local alternative of order n-1/2. Due to the unknown dependence of error terms and the estimation effects, a new block-wise random weighting method is constructed to bootstrap the critical values of the test statistic. The new method is easy to implement and its validity is justified. The theory is illustrated by a small simulation study and an application to S&P 500 stock index. © 2015 Elsevier B.V.postprin

Design, Search and Implementation of Improved Large Order Multiple Recursive Generators and Matrix Congruential Generators

Large order, maximum period multiple recursive generators (MRGs) with few nonzero terms (e.g., DX-k-s generators) have become popular in the area of computer simulation. They are efficient, portable, have a long period, and have the nice property of high-dimensional equi-distribution. The latter two properties become more advantageous as k increases. The performance on the spectral test, a theoretical test that provides some measure of uniformity in dimensions beyond the MRG\u27s order k, could be improved by choosing multipliers that yield a better spectral test value. We propose a new method to compute the spectral test which is simple, intuitive, and efficient for some special classes of large order MRGs. Using this procedure, we list \u27\u27better\u27\u27 FMRG-k and DX-k-s generators with respect to performance on the spectral test. Even so, MRGs with few nonzero terms do not perform as well with respect to the spectral test as MRGs with many nonzero terms. However, MRGs with many nonzero terms can be inefficient or lack a feasible parallelization method, i.e., a method of producing substreams of (pseudo) random numbers that appear independent. To implement these MRGs efficiently and in parallel, we can use an equivalent recursion from another type of generator, the matrix congruential generator (MCG), a k-dimensional generalization of a first order linear recursion where the multipliers are embedded in a k by k matrix. When MRGs are used to construct MCGs and the recursion of the MCG is implemented k at a time for a k-dimensional vector sequence, then the MCG mimics k copies of a MRG in parallel with different starting seeds. Therefore, we propose a method for efficiently finding MRGs with many nonzero terms from an MRG with few nonzero terms and then give an efficient and parallel MCG implementation of these MRGs with many nonzero terms. This method works best for moderate order k. For large order MRGs with many nonzero terms, we propose a special class called DW-k. This special class has a characteristic polynomial that yields many nonzero terms and corresponds to an efficient and parallel MCG implementation