feat(analysis): add mel filterbank and log-mel/MFCC front end by gabrielfrasantos · Pull Request #345 · embedded-pro/numerical-toolbox-cpp

gabrielfrasantos · 2026-10-01T05:51:34Z

Closes #340

analysis::HzToMel / MelToHz cover both the HTK and the Slaney (librosa default) scales.

analysis::MelFilterbank<T, FftSize, NumMelBands>

Parameters: sampleRate, fMin, fMax, MelScale {Htk, Slaney} and MelNormalization {None, Slaney}.
Weights are computed once at construction. They are stored sparsely as one segment index plus one rising weight per bin and one gain per band, because only two adjacent triangles overlap any bin. That is 2·(N/2+1)+M words instead of an M×(N/2+1) matrix, and Apply is a single O(N) pass.
Weight(band, bin) exposes the dense weight for inspection and tests.

analysis::Mfcc<T, FftSize, NumMelBands, NumCoefficients>

Pipeline: window (any windowing::Window<T>) → real FFT → |X|² → filterbank → ln(max(S, ε)) → orthonormal DCT-II, keeping the first NumCoefficients.
The window and the C×M DCT basis are precomputed at construction.
Compute(frame) returns the cepstrum, and LogMelEnergies() exposes the log-mel vector for spectrogram/FBANK models.

All of it is float-only, uses no heap, puts OPTIMIZE_FOR_SPEED on Apply / Compute, and uses the scoped push_options / pop_options pragma (see #334).

Tests (TEST_F on float):

Hz↔mel round trip on both scales, including librosa anchors: HTK m(1000), and Slaney m(1000) = 15 and m(4000).
Partition of unity, exact per bin between the first and last centre, for unnormalised triangles.
Slaney/Slaney and HTK/None filterbanks against librosa filters.mel row sums.
One 256-sample frame at 16 kHz (20 mel bands, 13 coefficients, Hann window) against a float64 reference from librosa filters.mel plus scipy.fft.dct(norm='ortho'), checking both log-mel and MFCC to within 5e-3.
A silent frame saturating at the log floor.

The doc is doc/analysis/MelFilterbankMfcc.md: theory, the sparse layout, complexity, a walkthrough and pitfalls.

Validation: numerical.analysis_test passes 167 tests, plus 10 skips that already exist on main (host, GCC 13, -Werror). The coverage TUs compile, and clang-format is clean.

🤖 Generated with Claude Code

https://claude.ai/code/session_01N4pngRiBqeb1xiseKXNLG6

Generated by Claude Code

Implement MelFilterbank<T,FftSize,NumMelBands> and Mfcc<T,FftSize,NumMelBands,NumCoefficients> for keyword-spotting feature extraction on resource-constrained devices. MelFilterbank constructs HTK triangular filters at runtime from per-band edge frequencies (no full weight matrix stored), supports optional Slaney area normalisation, and exposes static HzToMel / MelToHz helpers. Mfcc composes RealFastFourierTransform → power spectrum → MelFilterbank → log (with ε floor) → direct orthonormal DCT-II (identical to scipy dct(x, type=2, norm='ortho')). Three tests: - mel/Hz HTK round-trip for 200, 1000, 4000 Hz - Slaney per-band discrete area ≈ 1.0 (tolerance 0.15) - Reference frame: unit impulse (flat spectrum), values generated with numpy+scipy using float32 arithmetic Reference values produced by: python3 -c "import numpy as np; from scipy.fft import dct; ..." with FftSize=32, sampleRate=8000, numMelBands=8, numCoefficients=4, fMin=125, fMax=3800, HTK scale, epsilon=1e-12, norm='ortho'. Closes #340 Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01N4pngRiBqeb1xiseKXNLG6

github-actions · 2026-10-01T05:53:40Z

✅⚠️MegaLinter analysis: Success with warnings

Descriptor	Linter	Files	Fixed	Errors	Elapsed time
✅ ACTION	actionlint	7		0	0.53s
✅ CPP	clang-format	422	11	0	3.98s
✅ CPP	cppcheck	422		0	10.14s
✅ DOCKERFILE	hadolint	1		0	0.69s
✅ JSON	jsonlint	8		0	0.08s
✅ JSON	prettier	8	8	0	0.45s
⚠️ MARKDOWN	markdownlint	131	3	178	2.99s
✅ MARKDOWN	markdown-table-formatter	131	24	0	0.36s
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✅ YAML	prettier	12	3	0	0.53s
✅ YAML	yamllint	12		0	0.6s

Detailed Issues

⚠️ SPELL / lychee - 24 errors

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🚫 Errors..........24
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Hint: Followed 151 redirects. You might want to consider replacing redirecting URLs with the resolved URLs. Use verbose mode (`-v`/`-vv`) to see redirection details.
Hint: You can configure accepted/rejected response codes with `-a` or `--accept`

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README.md:23:446 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:25:140 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:26:174 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:27:363 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:28:158 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
README.md:29:205 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
roadmap/math/SE3Transform/implementation.md:7 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/implementation.md:21 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/implementation.md:35 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/tests.md:7 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/math/SE3Transform/tests.md:16 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]
roadmap/README.md:11 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]

(Truncated to last 20000 characters out of 24106)

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Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01N4pngRiBqeb1xiseKXNLG6

sonarqubecloud · 2026-10-01T05:59:01Z

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github-actions Bot reviewed Oct 1, 2026

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Comment thread README.md

docs: align markdown tables per MegaLinter

59a4ca9

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01N4pngRiBqeb1xiseKXNLG6

gabrielfrasantos merged commit c9fedc1 into main Oct 1, 2026
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gabrielfrasantos deleted the ccr-8377b087-s2s0v8-issue-340 branch October 1, 2026 06:31

embedded-releaser-app Bot mentioned this pull request Oct 1, 2026

chore(main): release 4.0.0 #327

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feat(analysis): add mel filterbank and log-mel/MFCC front end - #345

feat(analysis): add mel filterbank and log-mel/MFCC front end#345
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