GloptiPoly 3: moments, optimization and
semidefinite programming.
Gloptipoly 3 is intended to solve, or at least approximate, the Generalized Problem of
Moments (GPM), an infinite-dimensional optimization problem which can be viewed as
an extension of the classical problem of moments [8]. From a theoretical viewpoint, the
GPM has developments and impact in various areas of mathematics such as algebra,
Fourier analysis, functional analysis, operator theory, probability and statistics, to cite
a few. In addition, and despite a rather simple and short formulation, the GPM has a
large number of important applications in various fields such as optimization, probability,
finance, control, signal processing, chemistry, cristallography, tomography, etc. For an
account of various methodologies as well as some of potential applications, the interested
reader is referred to [1, 2] and the nice collection of papers [5].
標簽：
optimization
semidefinite
programming
GloptiPoly
上傳時間：
2016-06-05
上傳用戶：lgnf
All inputs of the C16x family have Schmitt-Trigger input characteristics. These Schmitt-Triggers are intended to always provide proper internal low and high levels, even if anundefined voltage level (between TTL-VIL and TTL-VIH) is externally applied to the pin.The hysteresis of these inputs, however, is very small, and can not be properly used in anapplication to suppress signal noise, and to shape slow rising/falling input transitions.Thus, it must be taken care that rising/falling input signals pass the undefined area of theTTL-specification between VIL and VIH with a sufficient rise/fall time, as generally usualand specified for TTL components (e.g. 74LS series: gates 1V/us, clock inputs 20V/us).The effect of the implemented Schmitt-Trigger is that even if the input signal remains inthe undefined area, well defined low/high levels are generated internally. Note that allinput signals are evaluated at specific sample points (depending on the input and theperipheral function connected to it), at that signal transitions are detected if twoconsecutive samples show different levels. Thus, only the current level of an input signalat these sample points is relevant, that means, the necessary rise/fall times of the inputsignal is only dependant on the sample rate, that is the distance in time between twoconsecutive evaluation time points. If an input signal, for instance, is sampled throughsoftware every 10us, it is irrelevant, which input level would be seen between thesamples. Thus, it would be allowable for the signal to take 10us to pass through theundefined area. Due to the sample rate of 10us, it is assured that only one sample canoccur while the signal is within the undefined area, and no incorrect transition will bedetected. For inputs which are connected to a peripheral function, e.g. capture inputs, thesample rate is determined by the clock cycle of the peripheral unit. In the case of theCAPCOM unit this means a sample rate of 400ns @ 20MHz CPU clock. This requiresinput signals to pass through the undefined area within these 400ns in order to avoidmultiple capture events.For input signals, which do not provide the required rise/fall times, external circuitry mustbe used to shape the signal transitions.In the attached diagram, the effect of the sample rate is shown. The numbers 1 to 5 in thediagram represent possible sample points. Waveform a) shows the result if the inputsignal transition time through the undefined TTL-level area is less than the time distancebetween the sample points (sampling at 1, 2, 3, and 4). Waveform b) can be the result ifthe sampling is performed more than once within the undefined area (sampling at 1, 2, 5,3, and 4).Sample points:1. Evaluation of the signal clearly results in a low level2. Either a low or a high level can be sampled here. If low is sampled, no transition willbe detected. If the sample results in a high level, a transition is detected, and anappropriate action (e.g. capture) might take place.3. Evaluation here clearly results in a high level. If the previous sample 2) had alreadydetected a high, there is no change. If the previous sample 2) showed a low, atransition from low to high is detected now.
標簽：
Signal
Input
Fall
Rise
上傳時間：
2013-10-23
上傳用戶：copu
