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Excuse my silly question, but i really want to know does changing the sampling rate affects the energy (bandwidth) of a signal? therefore improves cross correlation output?

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You must observe the nyquist frequency when sampling a signal. In order to sample a signal without introducing artifacts, you must first filter out everything in the signal that has a frequency higher than half of your sampling rate. If you sample a 1000Hz, then you must first filter out everything above 500Hz.

Yes, changing the sampling rate can change the bandwidth of digital representation of the signal. A lower sampling rate means a smaller bandwidth.

This will only improve crosscorrelation if the noise is all high frequency stuff, and the signal you are trying to detect is in the lower frequencies. You could get the same effect, however, by using a low pass filter on the sampled data. That would also remove the high frequencies and make the correlation clearer.

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  • $\begingroup$ in my case i have a signal at 20KHz, and some background noise with lower frequencies. i tried 44.1khz and 48khz. i found that 48khz is better after cross correlation. can you explain to me more please? "A lower sampling rate means a smaller bandwidth."? $\endgroup$ – hanaa Aug 18 '14 at 9:17
  • $\begingroup$ "Bandwidth" in its simplest form means "the range of frequencies in the signal." If you sample at 44.1kHz, then your digitized signal can contain frequencies between 0 and 22050 Hz. It has a bandwidth of 22050 Hz. If you sample at 48KHz, then your digitized signal has frequencies from 0 to 24KHz, a bandwidth of 24KHz. 20KHz is very close to the cutoff of 22050 when sampling at 44.1KHz. The signal you wanted to look at was getting partially destroyed by the anti-aliasing filters. When you switched to 48KHz, the antaliasing filter changed and more of your real signal got through. $\endgroup$ – JRE Aug 18 '14 at 9:30
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For example, if you double the sampling rate, energy will be boosted by 3db. But power will remain same. Simply, because you have now double samples.

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