I'm trying really hard to understand the segment of text from a standard communication book ( Modern digital and analog communications by B P Lathi). We are trying to find the power spectral density of binary signalling where the value can take random values 1,0,-1 with probabilities given. What I understand is that to find the power spectral density the very first step is to find Correlation of the random values . I'm not able to understand the method . I understood how the mean and variance is found , but not how Correlation for 1 is found and why does Correlation for greater than or 2 be zero. Could someone please explain an alternate simple method or bother to please explain the same method ?
The correlation for greater than 1 is 0 because each bit in the chain is independent of the last bit. For example were the current bit a 1, the probability of the next bit being a 1 is just 50/50. Were the current bit a -1, the probability of the next bit being a 1 is still 50/50.