Analysis of Autocorrelation Functions in Colored Noise

The second figure presents a graphical representation of the autocorrelation functions associated with four distinct types of colored noise. Both 'red noise' and 'blue noise' demonstrate positive autocorrelation, with 'red noise' exhibiting a characteristic of long-range autocorrelation. This means that its autocorrelation function maintains a positive value over an extensive range. Conversely, 'blue noise' and 'violet noise' display short-range negative autocorrelation. Their autocorrelation functions exhibit a rapid decay to zero, accompanied by small-scale fluctuations. Consequently, it is suggested that 'red noise' possesses a degree of pseudo-periodicity. This pseudo-periodicity may potentially exert an influence on the decoherence properties of the system under investigation.