Now that we've identified the audio sample damaged by the click (whose true values are unknown), we need to estimate the unknown samples. First we start by finding P coefficients a[i] for the autoregressive model, which is:

(1)

where s[n] is the signal value for the sample number n, and e[n] is the error term of the autoregressive model for sample n. For a simple example we'll let P=2 and n=6. The coefficients are determined using ordinary least squares techniques using good samples before and behind the unkown section. (1) can be rearranged:

(2)

This can be further written in matrix notation as:

**e = A * s**

**s** (the original row vector of signal data) is modified, so
that all the unknown sample values are set to zero, i.e. **s**
= [s1 s2 0 0 s5 s6 ].

**A** is constructed so the product **A * s** will produce
(2):

**A =
**

**Au** is now constructed from the columns in **A** corresponding
to the unknown signal columns in **s:**

**Au** =

(And then a matrix algebra miracle occurs), ``the minimum variance
unbiased missing estimator for the missing data
^{1}'' is