Analyses for equivalent ratio model in measurements of high standard resistance bridges

Presso l'Istituto Nazionale di Ricerca Metrologica (INRiM) è stata effettuata una prima valutazione esplorativa di un modello a rapporto equivalente per un ponte commerciale a doppia sorgente utilizzando regole di triangolazione metrologica restrittive. Lo studio è stato condotto osservando le misure di rapporto di resistenze campione nel campo da 10 Tohm a 1 Pohm.At the National Institute of Metrological Research (INRiM), a first evaluation of an exploratory method in the equivalent ratio model for a commercial dual source, high resistance bridge has been made using restrictive metrological triangulation rules. The study was performed observing the ratios measurements of a commercial bridge for the standard resistors in the range from 10 Tohm to 1 Pohm

Statistical tools for analysis of the performance of a high resistance measurement bridge

Il rapporto tecnico descrive l’utilizzo delle varianze di Allan e della densità di potenza spettrale per individuare le sorgenti di rumore che si possono riscontrare nel funzionamento del ponte di Wheatstone modificato di alta resistenza di tipo commerciale. Lo studio è stato condotto osservando le misure di corrente del detector del ponte in funzione del tempo di integrazione del medesimo. Da un’analisi preliminare dei dati ottenuti sono stati individuate le principali sorgenti di rumore del sistema in corrispondenza dei tempi di integrazione del detectorThe technical report exploits the use of Allan variances and the spectral power density to analyze the performance of the high resistance measurement Wheatstone modified bridge of commercial type. The study was performed by observing the current measurements of the bridge detector as a function of its integration time. From a preliminary analysis of the data obtained, the main sources of noise of the system have been identified in correspondence with the integration times of the detector

A Statistical Analysis of Multipath Interference for Impulse Radio UWB Systems

In this paper, we develop a statistical characterization of the multipath interference in an Impulse Radio (IR)-UWB system, considering the standardized IEEE 802.15.4a channel model. In such systems, the chip length has to be carefully tuned as all the propagation paths located beyond this limit can cause interframe/intersymbol interferences (IFI/ISI). Our approach aims at computing the probability density function (PDF) of the power of all multipath components with delays larger than the chip time, so as to prevent such interferences. Exact analytical expressions are derived first for the probability that the chip length falls into a particular cluster of the multipath propagation model and for the statistics of the number of paths spread over several contiguous clusters. A power delay profile (PDP) approximation is then used to evaluate the total interference power as the problem appears to be mathematically intractable. Using the proposed closed-form expressions, and assuming minimal prior information on the channel state, a rapid update of the chip time value is enabled so as to control the signal to interference plus noise ratio.Comment: 17 pages, 9 figures; submitted to the Journal of the Franklin Institute on Sept. 24, 201

Measurement Method for Evaluating the Probability Distribution of the Quality Factor of Mode-Stirred Reverberation Chambers

An original experimental method for determining the empirical probability distribution function (PDF) of the quality factor (Q) of a mode-stirred reverberation chamber is presented. Spectral averaging of S-parameters across a relatively narrow frequency interval at a single pair of locations for the transmitting and receiving antennas is applied to estimate the stored and dissipated energy in the cavity, avoiding the need for spatial scanning to obtain spatial volume or surface averages. The effective number of simultaneously excited cavity modes per stir state, M, can be estimated by fitting the empirical distribution to the parametrized theoretical distribution. The measured results support a previously developed theoretical model for the PDF of Q and show that spectral averaging over a bandwidth as small as a few hundred kHz is sufficient to obtain accurate results.Comment: submitted for publicatio

Fast hashing with Strong Concentration Bounds

Previous work on tabulation hashing by Patrascu and Thorup from STOC'11 on simple tabulation and from SODA'13 on twisted tabulation offered Chernoff-style concentration bounds on hash based sums, e.g., the number of balls/keys hashing to a given bin, but under some quite severe restrictions on the expected values of these sums. The basic idea in tabulation hashing is to view a key as consisting of $c=O(1)$ characters, e.g., a 64-bit key as $c=8$ characters of 8-bits. The character domain $\Sigma$ should be small enough that character tables of size $|\Sigma|$ fit in fast cache. The schemes then use $O(1)$ tables of this size, so the space of tabulation hashing is $O(|\Sigma|)$. However, the concentration bounds by Patrascu and Thorup only apply if the expected sums are $\ll |\Sigma|$. To see the problem, consider the very simple case where we use tabulation hashing to throw $n$ balls into $m$ bins and want to analyse the number of balls in a given bin. With their concentration bounds, we are fine if $n=m$, for then the expected value is $1$. However, if $m=2$, as when tossing $n$ unbiased coins, the expected value $n/2$ is $\gg |\Sigma|$ for large data sets, e.g., data sets that do not fit in fast cache. To handle expectations that go beyond the limits of our small space, we need a much more advanced analysis of simple tabulation, plus a new tabulation technique that we call \emph{tabulation-permutation} hashing which is at most twice as slow as simple tabulation. No other hashing scheme of comparable speed offers similar Chernoff-style concentration bounds.Comment: 54 pages, 3 figures. An extended abstract appeared at the 52nd Annual ACM Symposium on Theory of Computing (STOC20