Help~~ How it can spilt signal into 2 bands?

In 3gpp Ts 26.094, the famous GSM AMR specifications, VAD section, it
says,

Xlp(i) = 0.5*( A1(x(i-1)) + A2(x(i)) ) ;

Xhp(i) = 0.5*(A1(x(i-1)) - A2(x(i)) ) ;

where, A1 and A2 are first order direct form all-pass filters, whose
transfer function is given by

A(Z) = [C+Z^(-1)] / [1+C*Z^(-1)];

where , C is the filter coefficient. And, x(i) refer to as input
signal for filter bank, xlp(i) and xhp(i)

refer to as low pass component and high pass component respectively.


Why? What is the algo's principle?

Any comments are appreciated!

cheers
hyeewang