Fix the syntax in docs

This commit is contained in:
2026-09-07 11:12:04 +08:00
parent 7da3a5eb95
commit b619dee523
6 changed files with 163 additions and 147 deletions
+14 -7
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@@ -109,8 +109,12 @@ The strict importer currently accepts:
- an explicitly free-field/anechoic `RoomType`.
Receiver order comes from geometry, never from the receiver array index. SOFA
listener coordinates are $+X$ front, $+Y$ left, $+Z$ up; ADM coordinates are
$+X$ right, $+Y$ front, $+Z$ up:
listener coordinates are $+X$ front,
$+Y$ left,
$+Z$ up; ADM coordinates are
$+X$ right,
$+Y$ front,
$+Z$ up:
$$\bigl(x_{\mathrm{SOFA}},\ y_{\mathrm{SOFA}},\ z_{\mathrm{SOFA}}\bigr) = \bigl(y_{\mathrm{ADM}},\ -x_{\mathrm{ADM}},\ z_{\mathrm{ADM}}\bigr)$$
@@ -159,7 +163,8 @@ The fixed resource is `data/rosella_kernels.npz`, which implements publicly
standardized filter banks, computable from the following formulas.
The hybrid analysis kernels are defined in [3GPP TS 26.405 / ETSI TS 126 405](https://www.etsi.org/deliver/etsi_ts/126400_126499/126405/06.00.00_60/ts_126405v060000p.pdf),
Section 5.2.2 (Table 1 $Q=8$/$Q=4$ coefficients, delay 6):
Section 5.2.2 (Table 1 $Q=8$/
$Q=4$ coefficients, delay 6):
$$G_q^p[n] = g^p[n]\cdot\exp\!\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr),\qquad n=0,\dots,12$$
@@ -170,17 +175,19 @@ reordering of the public 640-tap prototype $c_0,\dots,c_{639}$:
$$A_{r,t} = \frac{(-1)^t}{128}\,c_{63-r+64t},\qquad r=0,\dots,63,\ t=0,\dots,9$$
The QMF synthesis table is the causal left inverse of the analysis polyphase
matrix $\mathbf{A}$, i.e. the solution of $\mathbf{A}\,\mathbf{W}=\mathbf{P}$
matrix $\mathbf{A}$, i.e. the solution of
$\mathbf{A}\,\mathbf{W}=\mathbf{P}$
($\mathbf{P}$ is the 577-sample delay permutation; total latency
$961 = 577 + 6\times64$), stored as a rank-4 factorization:
$$W_{b,l} = \sum_{r=1}^{4} t_{b,l,r}\,\mathbf{b}_{b,r}^{\top}$$
The hybrid synthesis table is the 77→64 recombination: identity for the high
bands, $Y_{3+b}=X_{16+b}$, and for the low bands ($C_p$ is the $8+4+4$ child
partition):
bands, $Y_{3+b}=X_{16+b}$, and for the low bands(
$C_p$ is the
$8+4+4$ child partition):
$$Y_p = \sum_{q\in C_p}\Bigl(\operatorname{Re}X_q + j\,s_q\,\operatorname{Im}X_q\Bigr),\qquad s_q\in\{\pm1\}$$
$$Y_p = \sum_{q\in C_p}\Bigl(\mathrm{Re}X_q + j\,s_q\,\mathrm{Im}X_q\Bigr),\qquad s_q\in\{\pm1\}$$
The loader verifies the archive and every array by SHA-256; the table version,
all array hashes, and the 77 reference band-center values are part of the cache