4.1.3 Fixed Point Lattice Technique (FLAT)
3GPP46.020Half rate speechHalf rate speech transcodingRelease 17TS
Let rj represent the jth reflection coefficient. The FLAT algorithm for the determination of the reflection coefficients is stated as follows:
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STEP 1 |
Compute the covariance (autocorrelation) matrix from the input speech: 0 £ i, k £ Np (5) |
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STEP 2 |
The (i,k) array is modified by windowing EMBED Equation 0 £ i, k £ Np (6) |
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STEP 3 |
0 £ i, k £ Np – 1 (7) 0 £ i, k £ Np – 1 (8) 0 £ i, k £ Np – 1 (9) |
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STEP 4 |
set j = 1 |
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STEP 5 |
Compute rj EMBED Equation (10) |
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STEP 6 |
If j = NP then done. |
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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) |
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STEP 8 |
j = j+1 |
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STEP 9 |
go to step 5. |
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The windowing coefficients, w(|i-k|), are found in the table 1.
Table 1: Windowing coefficients
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w(0) |
0,998966 |
w(5) |
0,974915 |
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w(1) |
0,996037 |
w(6) |
0,969054 |
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w(2) |
0,991663 |
w(7) |
0,963060 |
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w(3) |
0,986399 |
w(8) |
0,956796 |
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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.