Sampling low pass filtered white noise

AI Thread Summary
Filtering ideal white noise with a low-pass filter (LPF) and sampling it at a frequency F Hz affects the statistical behavior of the output signal. If the sampling frequency is less than the Nyquist frequency, the resulting discrete signal will be correlated. As the sampling frequency approaches or exceeds the Nyquist frequency, the output can become uncorrelated or statistically independent. The conditions for orthogonality depend on the specific relationship between the cutoff frequency of the LPF and the sampling frequency. Understanding these relationships is crucial for analyzing the output signal's statistical properties.
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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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