Autocorrelation of a Shifted Sequence

1. How do you find the autocorrelation of a sequence?
2. What is sequence autocorrelation?
3. What is autocorrelation in PN sequence?
4. What is the autocorrelation of a sampling function?

How do you find the autocorrelation of a sequence?

Definition 1: The autocorrelation function (ACF) at lag k, denoted ρ_k, of a stationary stochastic process, is defined as ρ_k = γ_k/γ₀ where γ_k = cov(y_i, y_i+k) for any i. Note that γ₀ is the variance of the stochastic process. The variance of the time series is s₀. A plot of r_k against k is known as a correlogram.

What is sequence autocorrelation?

The autocorrelation function (ACF), as defined by Equation 6.6, is the average product of the sequence x[n] with a time shifted m, version of itself. Autocorrelation is a valuable measure of the statistical dependence between values of x[n] at different times, and summarises its time- domain structure.

What is autocorrelation in PN sequence?

A PN code is a sequence of binary numbers with certain autocorrelation properties. These sequences are typically periodic. A maximum-length sequence is a periodic PN sequence with the longest possible period for a given length M of the shift register. The period of such a sequence is N=2^M−1.

What is the autocorrelation of a sampling function?

Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them.