Sampling low pass filtered white noise

In summary, the conversation discusses the effects of filtering out ideal white noise using an ideal LPF and then sampling it at different frequencies. The conditions for different sampling frequencies are mentioned, such as correlation, uncorrelation, statistical independence, and orthogonality. The speaker expresses interest in understanding the statistical behavior of the resulting discrete signal. The suggested resource provides further information on the topic.
  • #1
dexterdev
194
1

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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  • #2
The following summary addresses your questions:

http://www.eas.uccs.edu/wickert/ece5650/lectures/N5650_4.pdf
 
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  • #3
@njoysci : Thank you very much. Let me read it.
 

1. What is low pass filtered white noise?

Low pass filtered white noise is a type of noise signal that has been filtered to remove high frequency components, leaving only low frequency components. It is characterized by a random distribution of values with equal energy at all frequencies below a certain cutoff point.

2. Why is sampling low pass filtered white noise important?

Sampling low pass filtered white noise is important because it allows for the creation of a discrete signal that can be used for various applications, such as signal processing, communication systems, and data analysis. It also helps to reduce the amount of data that needs to be processed, making it more efficient for analysis.

3. How is low pass filtered white noise sampled?

Low pass filtered white noise is typically sampled using an analog-to-digital converter (ADC), which converts the continuous signal into a series of discrete values at regular time intervals. The sampling rate used must be at least twice the cutoff frequency of the noise signal in order to accurately capture its characteristics.

4. What are the potential challenges when sampling low pass filtered white noise?

One potential challenge when sampling low pass filtered white noise is aliasing, which occurs when the sampling rate is not high enough and high frequency components of the signal are mistakenly captured as low frequency components. Another challenge is the presence of other noise sources or interference, which can affect the accuracy of the sampled signal.

5. How can the accuracy of sampling low pass filtered white noise be improved?

The accuracy of sampling low pass filtered white noise can be improved by using a higher sampling rate, which reduces the chances of aliasing. It is also important to properly filter out any other noise sources or interference before sampling, and to use a high-quality ADC with sufficient resolution to accurately capture the signal. Additionally, signal processing techniques can be used to further improve the accuracy of the sampled data.

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