The decoder took ~70s for a 20-minute recording. Profiling revealed the
bottleneck was not the 6400-candidate cycle-offset search, but the
cepstrum filter's naive O(N²) DCT calling math.Cos() in the inner loop:

 55458 STFT frames × 2 passes × 256² × math.Cos() = 7.27 billion calls
 At ~20ns per call: ~145 seconds (dominated total runtime)

Fixes:

 1. Precomputed cosine table: compute 256×256 = 65536 cosine values
 once, then use table lookups in the inner loop. Eliminates all
 math.Cos() calls from the per-frame processing.

 2. Parallel cycle-offset search: 5 goroutines (one per rep offset),
 each searching 1280 cycle offsets independently. The rep offsets
 are fully independent — no shared state, no synchronization needed
 until the final result merge.

 3. Precomputed center-frame lists: instead of checking f%timeRep for
 every frame in every candidate test, precompute which frames are
 center frames for each rep offset. Eliminates per-frame branching.

 4. Float64 PN chip arrays: convert int8 PN chips to float64 once at
 startup. Eliminates int8→float64 conversion in the hot inner loop
 (204 conversions × 11000 frames × 6400 candidates = 14.4 billion
 avoided conversions).

Performance (20-minute recording, 55458 STFT frames):

 Before: 70s (math.Cos dominated)
 After: 11.5s (6x faster)
 Unit test (round-trip): 20s → 1.4s (14x faster)

Note: attempted coarse/fine search (testing every 10th group offset,
then refining) but abandoned — the chi-squared metric peak is too
narrow and the coarse step missed the true peak, causing false
positives. The full 6400-candidate brute-force search is kept for
correctness; the speedup comes entirely from eliminating per-operation
overhead, not from reducing the number of operations.

Complete redesign of the audio watermark system. The previous time-domain
PN chip correlator failed over the FM air channel due to non-linear clock
drift between TX and RX sample clocks, destroying bit-boundary alignment
and producing ~50% BER (random).

The new system embeds the watermark in STFT magnitudes (frequency domain),
eliminating all sample-clock sensitivity. Based on:

 D. Kirovski, H.S. Malvar, "Spread-Spectrum Watermarking of Audio Signals"
 IEEE Trans. Signal Processing, Vol. 51, No. 4, April 2003

Architecture:

 Encoder (generator.go, two-pass):
 Audio → Stages 1-3 (LPF, drive, clip, cleanup)
 → Decimate ÷19 → 12 kHz mono
 → STFT (512-point Hann, hop=256, 21ms frames)
 → Magnitude × (1 ± 0.059) per PN chip (0.5 dB, multiplicative)
 → ISTFT → difference → ZOH ×19 → interpolation LPF@5.5kHz
 → add to L/R → Stages 4-6 (stereo encode, composite clip, pilot, RDS)

 Decoder (wmdecode, key-free):
 Recording → LPF@5.5kHz → decimate to 12 kHz
 → STFT (same parameters)
 → Cepstrum filter (DCT, zero first 8 coefficients → -6 dB carrier noise)
 → Cycle-offset search (6400 candidates, ~70s for 20-min recording)
 → PN correlation → 128 soft bit decisions
 → RS(16,8) Vandermonde decode → 64-bit fingerprint

Key properties:

 - Multiplicative embedding: watermark scales with audio content.
 Loud audio masks stronger watermark, silence gets zero watermark.
 No gate needed (old system required silence gate to prevent audibility).
 - Block repetition R=5: each PN chip repeated across 5 consecutive
 STFT frames. Detection uses center frame only. Tolerates ±2 frames
 (±43ms) of timing drift without any clock recovery.
 - Fixed PN sequence: spreading code is public (seed "fmrtx-stft-pn-v1"),
 enabling blind fingerprint extraction without knowing the license key.
 Key identity is carried solely in the RS-encoded payload.
 - PCC covert channel: PN partitioned into 128 subsets (one per data bit),
 permuted across the watermark cycle for localized-damage resilience.

Parameters:

 WMRate: 12000 Hz (228000/19, 192000/16 — exact both sides)
 FFT: 512-point, Hann window, hop=256 (50% overlap)
 Sub-band: bins 9-213 (200-5000 Hz), 204 frequency chips/frame
 Embedding: 0.5 dB (multiplicative, 0.00 dB RMS change on audio)
 Spreading: 204 bins × 10 groups/bit = 2040 chips/bit (33 dB gain)
 Block rep: R=5 (±2 frame drift tolerance)
 Payload: RS(16,8) → 64 bit fingerprint (SHA-256 truncated)
 WM cycle: 136.5 seconds
 Decode margin: ~19 dB over noise floor at 0.5 dB embedding

Over-the-air results (PlutoSDR TX → SDRplay RX, 102.8 MHz):

 BER: 0/128
 Erasures: 0
 avg|c|: 2260
 Spectrum: clean, no artifacts above 6 kHz

Bug fixes included:

 - RS decoder: replaced Forney formula (used α^pos instead of α^(15-pos)
 due to polynomial convention mismatch) with Vandermonde Gaussian
 elimination solver. The Horner-method syndrome computation uses
 C(x) = c[0]x^15 + ... + c[15], mapping byte position j to polynomial
 power (15-j). Forney was using α^j as the error locator instead of
 α^(15-j), producing wrong correction magnitudes for all erasure
 configurations.

 - Generator decimation: anti-alias LPF was applied only to every 19th
 sample instead of all composite-rate samples. IIR filter state was
 updated only at 12 kHz effective rate, producing incorrect filtering.
 Fixed: LPF processes all 228 kHz samples, then decimate.

 - ZOH spectral images: zero-order hold upsample (12k→228k) created
 images at 12k, 24k, 36k Hz, leaking into pilot/stereo-sub/RDS bands.
 Fixed: separate interpolation LPF@5.5kHz on the upsample path.

 - Detect() single-cycle bug: iterated over groups (one frame per group)
 instead of all recording frames. Longer recordings did not improve
 SNR. Fixed: iterate all frames with modular wrapping for automatic
 multi-cycle averaging.

New files:
 internal/dsp/fft.go Radix-2 Cooley-Tukey FFT/IFFT
 internal/watermark/stft_watermark.go STFT embedder + detector
 internal/watermark/stft_roundtrip_test.go

Changed files:
 internal/watermark/watermark.go RS Vandermonde fix, accessor methods
 internal/offline/generator.go Two-pass architecture, STFT overlay
 cmd/wmdecode/main.go Complete rewrite, key-free extraction
 cmd/fmrtx/main.go Remove old watermark log + import

Removed:
 Old time-domain Embedder, gate, pulse-shaping LPF, PN sequence,
 ChipRate/Level/RecordingRate constants, DiagnosticState

Add an STFT watermark path inspired by Kirovski & Malvar, including the frequency-domain embedder/decoder, FFT support, and round-trip coverage. Wire the generator and CLI tools to use the new analysis/synthesis flow for watermark experiments on the watermark-rework branch.