A.1 Simplified block filtering operation

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Consider an 8th order transversal filter with filter coefficients a₀..a₈, through which a signal is being passed, the output of the filter being:

(1)

If we apply block filtering over 20 ms segments, then this equation becomes:

(2)

If the energy of the filtered signal is then obtained for every 20 ms segment, the equation for this is:

(3)

We know that (see GSM 06.10, subclause 3.1.4):

(4)

If equation (3) is expanded and acf₀..acf₈ are substituted for sn then we arrive at the equations:

(5)

Where:

(6)