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==Description of NVGate Computation== | |||
===Introduction=== | |||
This document describes the different computations that are done inside the OR25 analyzer. | This document describes the different computations that are done inside the OR25 analyzer. | ||
===Computation of FFT=== | |||
For each record of signal with duration of T , the corresponding Fourier Transform is computed as: | For each record of signal with duration of T , the corresponding Fourier Transform is computed as: | ||
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[[Image:formula_01.png|framed|none]] | [[Image:formula_01.png|framed|none]] | ||
===Analysis Windows=== | |||
Analysis windows are defined in the OROS analyzer as follows: | Analysis windows are defined in the OROS analyzer as follows: | ||
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[[Image:formula_02.png|framed|none]] | [[Image:formula_02.png|framed|none]] | ||
===Computation of Spectra in Spectral Averaging=== | |||
[[Image:formula_03.png|framed|none]] | [[Image:formula_03.png|framed|none]] | ||
=== Computation of Spectra in Time Averaging=== | |||
Instantaneous auto spectrum and instantaneous cross spectrum are computed as for spectral averaging. | Instantaneous auto spectrum and instantaneous cross spectrum are computed as for spectral averaging. | ||
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[[Image:formula_04.png|framed|none]] | [[Image:formula_04.png|framed|none]] | ||
===Linear, Exponential, Peakhold and Referenced Peakhold Averaging=== | |||
If user has selected M averages, the successive averages are computed as follows: | If user has selected M averages, the successive averages are computed as follows: | ||
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[[Image:formula_05.png|framed|none]] | [[Image:formula_05.png|framed|none]] | ||
===Time Integration or Derivation of Spectra=== | |||
Auto and cross spectra can be modified in order to get the same effect as a single or double integration or derivation in time domain. | Auto and cross spectra can be modified in order to get the same effect as a single or double integration or derivation in time domain. | ||
[[Image:formula_06.png|framed|none]] | [[Image:formula_06.png|framed|none]] | ||
===Scaling of Auto and Cross Spectra=== | |||
Basically auto spectra and cross spectra are internally scaled in EU² relative to a pure sine signal (EU stands for Engineering Unit, which is the physical unit of the analyzed signal). | Basically auto spectra and cross spectra are internally scaled in EU² relative to a pure sine signal (EU stands for Engineering Unit, which is the physical unit of the analyzed signal). | ||
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For example, if user injects an 1 EU rms pure sine at a frequency exactly equal to one of the FFT lines, the corresponding line for I<sub>xx</sub>, I<sub>xy</sub>, G<sub>xx </sub>and G<sub>xy </sub>is equal to 1 EU². | For example, if user injects an 1 EU rms pure sine at a frequency exactly equal to one of the FFT lines, the corresponding line for I<sub>xx</sub>, I<sub>xy</sub>, G<sub>xx </sub>and G<sub>xy </sub>is equal to 1 EU². | ||
===Display of Auto and Cross Spectra=== | |||
Auto spectrum and cross-spectrum module can be displayed relatively to Amplitude or Power Spectrum Density. | Auto spectrum and cross-spectrum module can be displayed relatively to Amplitude or Power Spectrum Density. | ||
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[[Image:formula_07.png|framed|none]] | [[Image:formula_07.png|framed|none]] | ||
===Computation of frequency band power=== | |||
[[Image:formula_08.png|framed|none]] | [[Image:formula_08.png|framed|none]] | ||
===Computation of auto-correlation and cross-correlation=== | |||
[[Image:formula_09.png|framed|none]] | [[Image:formula_09.png|framed|none]] | ||
===Frequency Response Measurement=== | |||
From two auto spectra and the associated cross spectrum, the analyzer can compute the frequency response of a linear system. Two cases are considered for result interpretation, without or with extra measurement noises. | From two auto spectra and the associated cross spectrum, the analyzer can compute the frequency response of a linear system. Two cases are considered for result interpretation, without or with extra measurement noises. | ||
====Without measurement noise==== | |||
[[Image:formula_10.gif|framed|none]] | [[Image:formula_10.gif|framed|none]] | ||
====With measurement noise:==== | |||
[[Image:formula_11.png|framed|none]] | [[Image:formula_11.png|framed|none]] | ||
====Real and Imaginary parts:==== | |||
[[Image:formula_12.png|framed|none]] | [[Image:formula_12.png|framed|none]] | ||
===D.14 Interpolation of Peaks in Spectra=== | |||
When analyzing a sinusoid using FFT, this one appears as a peak in the spectrum. | When analyzing a sinusoid using FFT, this one appears as a peak in the spectrum. | ||
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In the OROS analyzer, the frequency correction is computed, at user request, with a resolution equal to 1/32<sup>th </sup>of the analysis resolution Δf. | In the OROS analyzer, the frequency correction is computed, at user request, with a resolution equal to 1/32<sup>th </sup>of the analysis resolution Δf. | ||
===Cepstrum=== | |||
The Module Cepstrum display is available in the FFT analysis with option "diag". | The Module Cepstrum display is available in the FFT analysis with option "diag". | ||
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A high "quefrency" represents rapid fluctuations in the spectrum (small frequency spacings) and a low "quefrency" represents slow changes with quefrency (large frequency spacings). Note that the quefrency does not give information on the absolute frequency but only about frequency spacings. | A high "quefrency" represents rapid fluctuations in the spectrum (small frequency spacings) and a low "quefrency" represents slow changes with quefrency (large frequency spacings). Note that the quefrency does not give information on the absolute frequency but only about frequency spacings. | ||
===Measurement scalar Level=== | |||
[[Image:formula_16.png|framed|none]] | [[Image:formula_16.png|framed|none]] | ||