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