nx_chirp_ss.nx

nx_chirp_ss.nx -- Chirp Spread Spectrum modulation, re-derived from the public chirp-z transform (Cooley 1969, IEEE T-AU). This is the modulation layer that gives the Nishi physical layer the long-link low-SNR tolerance of LoRa-class radio WITHOUT touching LoRa's patented demodulator tricks. Substrate v1 parameters: - M = 4 symbols per chirp (2 bits/symbol, "SF=2") - N = 64 samples per chirp - inc_min .. inc_max in phase-units per sample define the swept band; the chirp ramps linearly across [inc_min, inc_max). For symbol s, the chirp's instantaneous chip index is (i + s * N/M) mod N. This is the cyclic-shift property that gives CSS its orthogonality across the M-ary alphabet. Decoding is by correlation against the M reference chirps; arg-max picks the symbol. Substrate-friendly: integer-only, square-wave reference, no FFT required at SF=2. Patent stance: linear-FM chirp modulation predates LoRa by decades (Klauder 1960 radar; Cooley 1969 chirp-z math; Costas 1984 chirp sequences). We re-derive from those public sources, not from LoRa. Per cardinal feedback-nishilang-mission-displace-cuda-directx-via- patent-clean-absorption: never copy reference code; absorb the math. genealogy_id: cooley_1969_chirp_z + klauder_1960_radar_chirp + costas_1984_frequency_hopping + nx_bfsk_q10 lineage_id: nishi_chirp_ss_q10 nx_safety_envelope: intended_use: "Chirp spread-spectrum comms primitive (Costas 1984 + LoRa-class linear FM chirp) -- low- power telemetry, mesh networking, recovery beacons" sil_target: SIL2 (comms reliability; chirp recovery in noisy channels gates safety telemetry transport) asil_target: QM dal_target: DAL C evidence: [Q10_fixed_point_deterministic,