Sampling low pass filtered white noise

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SUMMARY

This discussion focuses on the statistical behavior of a discrete signal obtained by sampling low pass filtered white noise. The key condition established is that if the sampling frequency (F) is less than the Nyquist frequency, the output signal will be correlated. The conversation references an ideal low pass filter (LPF) with a cutoff frequency of W Hz, emphasizing the importance of sampling frequency in determining the correlation, independence, and orthogonality of the resulting discrete signal.

PREREQUISITES
  • Understanding of low pass filters (LPF) and their cutoff frequency
  • Knowledge of Nyquist theorem and sampling frequency
  • Familiarity with concepts of correlation, independence, and orthogonality in signal processing
  • Basic statistical analysis of signals
NEXT STEPS
  • Research the Nyquist-Shannon sampling theorem
  • Explore the mathematical properties of low pass filters (LPF)
  • Study the statistical behavior of sampled signals in signal processing
  • Learn about correlation and independence in the context of discrete signals
USEFUL FOR

Signal processing engineers, students studying electrical engineering, and researchers analyzing the statistical properties of sampled signals.

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Homework Statement



If we filter out ideal white noise using an ideal LPF of cutoff frequency W Hz and then sample it at F Hz , What are the conditions for different F so that the resulting discrete signal is correlated, uncorrelated , statistically independent and orthogonal etc?
I would like to know the statistical behaviour of the output signal.


Homework Equations






The Attempt at a Solution



I don't know where to start. But I think that if sampling frequency is lesser than nyquist frequency, the output is correlated.
 
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The following summary addresses your questions:

http://www.eas.uccs.edu/wickert/ece5650/lectures/N5650_4.pdf
 
Last edited by a moderator:
@njoysci : Thank you very much. Let me read it.
 

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