It was shown by examples that when step (2) is omitted, the found minimum of α P, o p t is worse than in the case of the a priori utilization of the QCSA.Ī simulation example follows. Note that the use of the QCSA according to step (2) of Algorithm 4.2 prior to the deployment of an iterative algorithm as in step (3) is beneficial. Output: The optimal parameter values p o p t, the corresponding spectrum Σ P, o p t, and the essential spectrum Σ P, e s s, o p t with their abscissae α P, o p t and α P, e s s, o p t, respectively. If the eventual values of p meet (4.9), then set p o p t : = p else, set p o p t : = p ˜. Use the selected iterative algorithm starting with p 0 resulting from (2). This step gives rise to the current parameter values p 0. In every single step, check (4.9): if the condition becomes unsatisfied, then save p ˜ : = p 0. ![]() Take only poles right from α P, e s s (4.23) or those with a small modulus. 2.Īpply Algorithm 4.1 (i.e., the QCSA) until m = r. If Δ n u m ( s, p ) with p = ∅ and (4.9) does not hold, abandon the algorithm. Input: Closed-loop characteristic quasipolynomial Δ n u m ( s, p ), initially desired poles loci, optimization problem (4.16), selected numerical optimization algorithm. 4 Read more Navigate DownĪlgorithm 4.2 Spectral abscissa minimization Ordinate precision, on the other hand, says something fundamental about the quality of the measurement process and in general cannot be changed merely with post-processing. Only the significant digits count, and those digits represent the true precision of the ordinate.Īs with abscissa quantization, ordinates can be quantized more finely after the fact by applying interpolation techniques. As any elementary science student knows, adding more digits to your answer does not necessarily make your answer any more precise. All it says is how many digits are recorded. It says nothing about the precision of the measurement. Ordinate quantization, on the other hand, is the minimum interval between any two different ordinate measurements. If you want to talk quantitatively about measurements, you need to do your statistics homework. This sort of reasoning is related to hypothesis testing and is part of the realm of the science of statistics. The other 1% of the time they are different based on dumb luck. That is to say, if two measurements are more than 1% apart from each other, then 99% of the time this difference represents truly different distances. For example, I might be able to measure a distance to within 1% precision given a confidence level of 99%. One can never know for sure if two unequal measurement results are just caused by dumb luck or if they are “really” different, but one can say with some quantified confidence level that the difference wasn't a fluke. It's a parameter that includes repeatability and random noise that prevents us from being able to decide if two different measurement results are different because they are measuring two different true values of the measurand, or because random errors have produced the difference. In that sense, ordinate resolution is a specification of the precision in the ordinate. When speaking just about an ordinate in isolation, resolution can be defined as the statistical blurring caused by measurement uncertainty. The minimum interval possible between two unequal ordinate measurements by a measurement system when measuring a DUT. Nadovich, in Synthetic Instruments, 2005 Ordinate Quantization Interval
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