Only embed watermark chips in STFT bins where the audio signal provides
sufficient masking. Bins in spectral valleys (>25 dB below local peak
within ±4 bins) are skipped — the watermark would be audible there and
they contribute more carrier noise than signal to the correlation.

PAFM is applied in the encoder only. The decoder correlates all bins
unconditionally, because the FM channel alters the spectral shape —
masking decisions made at the encoder do not match the receiver's
spectrum. Skipped bins contribute zero watermark energy (the encoder
didn't modify them) and only carrier noise, which the cepstrum filter
already suppresses by ~6 dB.

On average ~60-70% of bins carry watermark energy per frame, matching
Kirovski's observation. The remaining bins are silent (multiplicative
embedding: magnitude × 1.0 = unchanged).

Over-the-air result (62-minute recording):
 avg|c| = 6286 (27 WM cycles averaged)
 BER = 0/128
 Erasures = 0

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.