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84 lines
3.7 KiB
Markdown
84 lines
3.7 KiB
Markdown
# Python runtime tables
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[中文](README.md)
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This directory contains static production tables. It does not contain user HRTFs.
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`tables.npz` contains the JOC core decoding tables:
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```text
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analysis_window float64[10,64]
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qmf5_window float64[640]
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joc_huff_code_coarse_generic int64[95,2]
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joc_huff_code_fine_generic int64[191,2]
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joc_huff_code_coarse_coeff_sparse int64[95,2]
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joc_huff_code_fine_coeff_sparse int64[191,2]
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joc_huff_code_5ch_pos_index_sparse int64[4,2]
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joc_huff_code_7ch_pos_index_sparse int64[6,2]
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```
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`src/joc_qmf.py` loads the QMF tables, while `src/joc_decode.py` loads the JOC Huffman trees. Python does not read C/C++ headers under `native/`.
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The corresponding native data are stored in `native/src/qmf_tables.h` and `native/src/joc_huffman_tables.h`. Changes on either side should update the other and be checked for value-by-value agreement.
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## Binaural rendering tables
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`rosella_kernels.npz` contains the fixed 64-QMF/77-hybrid tables used by the
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public SOFA binaural path:
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```text
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format_version little-endian int32[1]
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qmf_analysis_coefficients float32[64,10]
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hybrid_analysis_low_kernel float32[3,2,13,16,2]
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hybrid_synthesis_indices int16[154,4]
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hybrid_synthesis_values float32[154]
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qmf_synthesis_basis float64[64,4,128]
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qmf_synthesis_taps float64[64,10,4]
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```
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The float32 table values are promoted to float64 when loaded.
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`src/public_filterbank.py` verifies the archive and every array by SHA-256.
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Those hashes, the table version, and the 77 reference band-center values all
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participate in the `.jochrtf` cache key. The full analysis/synthesis latency is
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961 samples.
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The packaged tables implement publicly standardized filter banks, computable
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from the following formulas.
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The 64-QMF → 77-hybrid structure, the 13-tap low-band prototypes, and their
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half-bin complex modulation are defined in
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[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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$$G_q^p[n] = g^p[n]\cdot\exp\!\Bigl(j\,\frac{2\pi}{Q^p}\bigl(q+\tfrac12\bigr)(n-6)\Bigr),\qquad n=0,\dots,12$$
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The 64-band QMF analysis is the MPEG-4 AAC/SBR 64 complex QMF analysis bank of
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ISO/IEC 14496-3/AMD1:2003, subclause 4.B.18.2; the packaged $64\times10$ table
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is the polyphase 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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($\mathbf{P}$ 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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$$Y_p = \sum_{q\in C_p}\Bigl(\operatorname{Re}X_q + j\,s_q\,\operatorname{Im}X_q\Bigr),\qquad s_q\in\{\pm1\}$$
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The same values also appear in other public implementations of these standards
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(for example FFmpeg's `aacps_tablegen.h` and `aacsbrdata.h`).
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Public availability of a standard does not by itself grant permission to
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practice related patent claims.
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SOFA is the user-visible source of truth. A `.jochrtf` file is a disposable JOC
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compiled HRTF cache that can be rebuilt from SOFA. The cache contains
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transformed source-HRTF data and remains subject to the source SOFA/HRTF
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dataset's licence and redistribution restrictions.
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