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References

The papers and standards behind the algorithms, in the order the library builds on them: the FFT engines first, then short-time analysis, the perceptual scales, and the audio I/O standards. Single source of truth: docs/references.bib in the library repo; the same keys appear in the docstrings and kernel sources.

FFT algorithms

  • [cooley1965] Cooley, James W.; Tukey, John W. “An algorithm for the machine calculation of complex Fourier series.” Mathematics of Computation, 19(90), 297-301, 1965. doi
  • [rader1968] Rader, Charles M. “Discrete Fourier transforms when the number of data samples is prime.” Proceedings of the IEEE, 56(6), 1107-1108, 1968. doi
  • [bluestein1970] Bluestein, Leo I. “A linear filtering approach to the computation of discrete Fourier transform.” IEEE Transactions on Audio and Electroacoustics, 18(4), 451-455, 1970. doi

Short-time analysis and synthesis

  • [allen1977] Allen, Jont B.; Rabiner, Lawrence R. “A unified approach to short-time Fourier analysis and synthesis.” Proceedings of the IEEE, 65(11), 1558-1564, 1977. doi
  • [griffin1984] Griffin, Daniel W.; Lim, Jae S. “Signal estimation from modified short-time Fourier transform.” IEEE Transactions on Acoustics, Speech, and Signal Processing, 32(2), 236-243, 1984. doi
  • [harris1978] Harris, Fredric J. “On the use of windows for harmonic analysis with the discrete Fourier transform.” Proceedings of the IEEE, 66(1), 51-83, 1978. doi
  • [smith-sasp] Smith, Julius O., III. Spectral Audio Signal Processing. W3K Publishing, 2011. ISBN 978-0-9745607-3-1. online

The mel scale

  • [stevens1937] Stevens, S. S.; Volkmann, John; Newman, Edwin B. “A scale for the measurement of the psychological magnitude pitch.” The Journal of the Acoustical Society of America, 8(3), 185-190, 1937. doi
  • [slaney1998] Slaney, Malcolm. Auditory Toolbox Version 2. Technical Report 1998-010, Interval Research Corporation, 1998. online

The constant-Q transform

  • [brown1991] Brown, Judith C. “Calculation of a constant Q spectral transform.” The Journal of the Acoustical Society of America, 89(1), 425-434, 1991. doi
  • [brown1992] Brown, Judith C.; Puckette, Miller S. “An efficient algorithm for the calculation of a constant Q transform.” The Journal of the Acoustical Society of America, 92(5), 2698-2701, 1992. doi
  • [schorkhuber2010] Schörkhuber, Christian; Klapuri, Anssi. “Constant-Q transform toolbox for music processing.” Proceedings of the 7th Sound and Music Computing Conference, Barcelona, 2010.
  • [glasberg1990] Glasberg, Brian R.; Moore, Brian C. J. “Derivation of auditory filter shapes from notched-noise data.” Hearing Research, 47(1-2), 103-138, 1990. doi

Loudness and metering

  • [bs1770] International Telecommunication Union. ITU-R BS.1770-4: Algorithms to measure audio programme loudness and true-peak audio level. ITU, 2015. online
  • [ebur128] European Broadcasting Union. EBU R 128: Loudness normalisation and permitted maximum level of audio signals. EBU, 2023. online
  • [ebutech3341] European Broadcasting Union. EBU Tech 3341: Loudness metering: ‘EBU mode’ metering to supplement EBU R 128 loudness normalisation. EBU, 2016. Defines the minimum-requirement test signals the loudness conformance tests reproduce. online
  • [ebutech3342] European Broadcasting Union. EBU Tech 3342: Loudness range: a measure to supplement EBU R 128 loudness normalisation. EBU, 2016. The LRA algorithm (3 s short-term loudness, two-stage gating, 10th-95th percentile) and its test signals. online
  • [deman2018] De Man, Brecht. “Evaluation of implementations of the EBU R128 loudness measurement.” Audio Engineering Society Convention 145, 2018. Source of the analog-prototype K-weighting design that generalises the BS.1770 fixed-48 kHz coefficients to arbitrary sample rates. online
  • [steinmetz2021] Steinmetz, Christian J.; Reiss, Joshua D. “pyloudnorm: a simple yet flexible loudness meter in Python.” Audio Engineering Society Convention 150, 2021. Its EBU-signal test methodology is mirrored by the loudness tests. online
  • [ffmpeg-ebur128] FFmpeg developers. FFmpeg ebur128 audio filter. 2024. Independent EBU R128 implementation used as a cross-check oracle in the loudness tests. online

Audio I/O components

  • [soxr] Sykes, Rob; dofuuz (fork). The SoX Resampler library (soxr); dofuuz fork with PFFFT and SIMD paths. 2023. The vendored resampler behind quality="quick" through "very_high". online
  • [drlibs] Reid, David. dr_libs: single-file public-domain audio decoders (dr_wav, dr_mp3, dr_flac). 2024. online
  • [minimp3] lieff. minimp3: minimalistic MP3 decoder with sample-accurate seeking (minimp3_ex). 2021. online
  • [taglib] Wheeler, Scott; the TagLib authors. TagLib audio meta-data library. 2024. Backend for tags and cover art across ID3v1/v2, Vorbis comments, MP4 atoms and APE. online