Autocorrelation is a concept in statistics and signal processing used to measure the correlation of a signal with itself at different time lags. In other words, autocorrelation determines the similarity of the signal at one time point compared to previous time points. Formula # The autocorrelation of a signal \( x(t) \) at a time lag \( \tau \) is defined as: \[ R(\tau) = \mathbb{E}[x(t) \cdot x(t + \tau)] \] Where: ...
In signal processing, the concepts of stationary and non-stationary are used to describe the properties of a signal over time. Stationary Signal # A signal is called stationary if its statistical properties do not change over time. These statistical properties include mean, variance, and correlation functions. There are two types of stationarity: Weak Stationarity (or Wide-Sense Stationarity): The signal has a constant mean and variance over time, and the correlation function depends only on the time difference between two points, not on the specific time points themselves. ...