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With this result and assuming that we have received N samples of waveform x(n) that are statistically independent of each other, we can now design the likelihood ratio test as follows.
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Its principal function is to determine the precise energy and timing of the signal from discrete samples of the waveform, taken each period of the LHC clock (25 ns).
Fig. 20 A sample result of waveform observation by the PWE/WFC in EMIC burst mode from 08 01 05 to 08 01 55 UT on April 9, 2017.
Fig. 19 A sample result of waveform observation by the PWE/WFC in chorus burst mode from 11 10 54 to 11 11 24 UT on April 9, 2017.
The sampling of the waveform is performed at a rate up to 10 GS/s with the SAMPIC chip.
According to the traditional Shannon/Nyquist theorem, the sampling of such waveform should be at least twice of its maximum bandwidth to avoid aliasing [1].
The number of data is calculated as a sum of the sampling data points of waveform envelopes assigned for a block by the NMO correction.
Because the time of detection of the particle is not synchronized with the sampling of the waveforms, the S-WPIA interpolates the waveforms at the time tag of the particle.
A typical sample of the waveforms of the applied voltage and beam current collected by the different metallic rings is shown in Figure4b where the beam current profile for different rings has been measured.
Mean pressure was calculated as the arithmetic mean of the sample waveform sampled at a frequency of 500 Hz.
This work proposes the use of the time-tagged input waveform samples of PMU-like sensors, instead of output samples of PMUs, for estimation of both continuous-state and discrete state through diagnosis of fault modes in order to gain the speed and accuracy during severe transients.
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