Algorithm 1. Flowchart of lag1 ACF algorithm for noise identification.

$Done=False, d=0$

$While Not Done$

$Z_i=\frac{1}{M}{\displaystyle \sum }_{j=1}^M{X}_{\left(i-1\right)·M+j}$  $\left(i=1,2,3,\dots ,N\right)$

$\overline{Z}=\frac{1}{N}{\displaystyle \sum }_{i=1}^N{Z}_i$       $N=int\left(\frac{N_X}{M}\right)$

$r_1=\frac{{{\displaystyle \sum }}_{k=1}^{N-1}\left(Z_k-\overline{Z}\right)\left(Z_{k+1}-\overline{Z}\right)}{{{\displaystyle \sum }}_{k=1}^N{\left(Z_k-\overline{Z}\right)}^2}$  $\sigma =\frac{r_1}{1+r_1}$

$If d\ge d_{min} \&\left(\sigma <0.25|d\ge d_{max}\right)$

$p=round\left(2\sigma \right)-2d$

$Done=True$

$Else$

$Z_1=Z_2-Z_{1,}\dots ,Z_{N-1}=Z_N-Z_{N-1}$

$N=N-1, d=d+1$

$Endif$

$End While$