What is equal to the FT of the Autocorrelation function

1. What is Fourier transform of autocorrelation?
2. What is autocorrelation function formula?
3. What is the value of the autocorrelation function of lag order 1?
4. What is the unit of autocorrelation?

What is Fourier transform of autocorrelation?

R(τ)=∫∞−∞x(t)x∗(t−τ)dt. Statement − The autocorrelation property of Fourier transform states that the Fourier transform of the autocorrelation of a single in time domain is equal to the square of the modulus of its frequency spectrum.

What is autocorrelation function formula?

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.

What is the value of the autocorrelation function of lag order 1?

A lag 1 autocorrelation (i.e., k = 1 in the above) is the correlation between values that are one time period apart. More generally, a lag k autocorrelation is the correlation between values that are k time periods apart.

What is the unit of autocorrelation?

Normalized autocorrelations have no units because the units are divided out as part of the normalization process. Non-normalized autocorrelations have the original data's units squared.