What is ACF? ACF Full Form, explain

The ACF full form is auto-correlation function, which is a statistical measure of the relationship between two random variables (ACF).
The autocorrelation function (ACF) demonstrates the variation in the correlation between any two signal values as their distance from one another varies [16]. It is a measure of the memory of a stochastic process in the time domain and provides no insight into the frequency content of the process. In most cases, an error signal, denoted by et,

If the underlying stochastic process is stationary, then the previous expression for the ACF can be simplified to a time-independent form. A white-noise process is entirely uncorrelated if and only if the autocorrelation function has a value of unity at lag zero but zero at all other lags. In contrast, correlated processes like ARMA and ARIMA show a correlation between lagged observations by having non-zero values at lags other than zero. The detail signals of an ARMA (1, 1) process are approximately decorrelated at different scales, whereas the wavelet coefficients corresponding to a correlated process are not. It will be demonstrated later that the multiscale representation’s benefit will aid in enhancing denoising’s quality.

An overlapping integral of shifted and unshifted surface height profiles provides the auto-correlation function.

When m increases, we use fewer data to calculate an average since our sample size is constrained. Since there is just a single data point to average, the estimation is quite inaccurate for m = N 1. As a result, we tend to ignore m values that are quite large.

Indicators of how widely hills and valleys are spaced can be gleaned from the autocorrelation function (full form of ACF in Hindi).
With L representing the length of the sample and the distance traveled over the surface (Fig. 1.9). The maximum value of the normalized ACF (0) is 1, when is zero. Correlation weakens and approaches zero as approaches infinity. For large values of, the exponential curve is obtained by plotting () versus decays from unity to zero. The ACF can be roughly represented by an exponential decay function for many real-world surfaces. Insight into the horizontal distribution of roughness can be gleaned from the shape of the decay curve. The value of at which () = 0.1 is sometimes used as the definition of the correlation length l. This l has a much higher value for open texture surfaces than for closed ones (Fig. 1.10). Many surfaces with randomness are said to be well-fit by the straightforward exponential decay function defined by () = exp ( 2.3/l).