CO{sub 2} dial transmitter/receiver noise characterization and related correlated noise issues Page: 9 of 15
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Signal + White Noise
Noise Power Spectral Density
White
Frequency
r
r
0
rAveraged Signal
1
nSamples (n)
Signal + Correlated Noise
Noise Power Spectral Density
Averaged Signal
P
0
e
r1/f
WhiteFrequency
r
r
0
rSamples (n)
Figure 6. Illustration of Potential Degradation of Multi-Sample Averaged Signal Error Due to Correlated Noise.
4.1. Effects of correlated noise on multi-sample averaging: A numerical example
A numerical simulation of the effects of correlated noise follows. Referring to Figures 7-A through 7-C, a temopral
ensemble of 4 noise types x 100 independent traces x 2000 samples per trace were generated. The four types of noise are
composed of i) 100 % white noise, ii) 10 % correlated noise and 90 % white noise, iii) 50 % correlated noise and 50 %
white noise and iv) 50 % band-limited correlated noise and 50 % white noise. By a bounded noise spectrum, we mean that
the correlated noise returns to the white noise floor within the noise trace power spectral density. Each noise trace has a
zero mean with a standard deviation = 0.9 with the correlated source composed of 1/f noise (see Figure 7-A for example
traces). The corresponding ensemble averaged autocorrelations are plotted in Figures 7-B, and the ensemble averaged
multi-sample error reduction is shown in Figure 7-C. The following observations are worth emphasizing:
" White noise, as expected, produces a 4n reduction in the standard deviation when averaged over n samples.
" Correlated noise increases the number of averaged samples required to achieve a desired level of error.
" The magnitude of degradation (relative to 4n reduction efficiencies) due to correlated noise depends on the
amount of correlated noise present, its spectral content relative to the sampled signal and whether the noise
spectrum is bounded (compare the 50% band-limited noise case with the 50% unbound case).0
e
r1 -.
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Cooke, B.; Schmitt, M.; Goeller, R.; Czuchlewski, S.; Fuller, K.; Olivas, N. et al. CO{sub 2} dial transmitter/receiver noise characterization and related correlated noise issues, article, February 1, 1996; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc665633/m1/9/: accessed May 10, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.