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Suppose you sample a random variable X at frequency f, then band pass filter the resultant timestream between frequencies f1 and f2. Now consider the timestream after filtering to consist of samples of a new random variable Y. How is the band pass filter related to the pdf of Y?
I'm trying to understand how the rms of cross-correlation \[\rho_{x,y}(\tau)\] between 2 timestreams (both with mean zero) x(t) and y(t) of white noise decreases with the number of samples N in each timestream.
\[\rho_{x,y}(\tau) = \frac{\sigma_{x,y}^2}{\sigma_x \sigma_y} =...
I know that band limiting a single timestream of white noise will turn the autocorrelation function into a sinc function from a delta function.
But suppose I have 2 timestreams of band limited white noise, what effect does the band limiting have on their cross correlation? If I collect an...
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