spike(rust/fft): port compute_cross_correlation to Rust (#96) - #103
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Implements the FFT cross-correlation core from AudioSyncer.js (L145-186) as a standalone Rust library function. Uses rustfft — no C FFT bindings. The division by N in the final normalization is explicit because rustfft's inverse transform does not normalize, unlike the JS fft library which normalizes implicitly. Omitting the division would scale SNR comparisons in validate_peak (#98) incorrectly. The impulse test documents that IFFT(FA * conj(FB)) places a lag-K peak at index N-K (the circular negative-lag form). This matches the JS formula exactly and is consistent with how find_best_lag (#97) will interpret the correlation array. AC: all acceptance criteria from #96
S1: assert corr.len() == 128 in the impulse test so the output-length AC is falsified for non-trivial inputs (previously only the single-sample case had an explicit length check). S2: document the len >= 1 precondition on compute_cross_correlation — empty slices cause usize underflow on `len_a + len_b - 1`, which is outside the AC scope but worth noting for callers.
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Summary
next_power_of_twoandcompute_cross_correlationinspike/audio-sync/src/lib.rs, faithfully replicatingAudioSyncer.jsL145–186 usingrustfftspike/audio-sync/src/lib.rsper the hard constraintTests (5 inline
#[cfg(test)])next_power_of_two_known_valuescross_correlation_impulse_peak_at_kcross_correlation_identical_inputs_peak_at_zerocross_correlation_all_zeros_no_paniccross_correlation_single_sample_length_onecargo test --manifest-path spike/audio-sync/Cargo.toml— 5/5 pass.Notes
The impulse test asserts the peak at
N - K(notK).IFFT(FA × conj(FB))places a B-lags-A-by-K event at the circular negative-lag index N-K. The AC explicitly accepts this ("or N - K for negative lag"). A precondition doc comment notes that empty slices cause usize underflow.Closes #96
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