4.1.3 Fixed Point Lattice Technique (FLAT)

06.203GPPHalf rate speech transcodingTS

Let rj represent the jth reflection coefficient. The FLAT algorithm for the determination of the reflection coefficients is stated as follows:

STEP 1

Compute the covariance (autocorrelation) matrix from the input speech:

0 £ i, k £ Np (5)

STEP 2

The (i,k) array is modified by windowing

EMBED Equation 0 £ i, k £ Np (6)

STEP 3

0 £ i, k £ Np – 1 (7)

0 £ i, k £ Np – 1 (8)

0 £ i, k £ Np – 1 (9)

STEP 4

set j = 1

STEP 5

Compute rj

EMBED Equation (10)

STEP 6

If j = NP then done.

STEP 7

Update Fj(i,k), Bj(i,k), Cj(i,k) 0 £ i, k £ NP-j‑1

EMBED Equation (11)

EMBED Equation EMBED Equation , (12)

EMBED Equation (13)

STEP 8

j = j+1

STEP 9

go to step 5.

The windowing coefficients, w(|i-k|), are found in the table 1.

Table 1: Windowing coefficients

w(0)

0,998966

w(5)

0,974915

w(1)

0,996037

w(6)

0,969054

w(2)

0,991663

w(7)

0,963060

w(3)

0,986399

w(8)

0,956796

w(4)

0.980722

w(9)

0,950127

This algorithm can be simplified by noting that the ’, F and B matrices are symmetric such that only the upper triangular part of the matrices need to be computed or updated. Also, step 7 is done so that Fj(i,k), Bj(i‑1,k‑1), Cj(i,k‑1), and Cj(k,i‑1) are updated together and common terms are computed once and the recursion is done in place.