feat(spectool): add --wav decode, IMDCT, and roundtrip test

- spectool --wav <input.spec> <output.wav>: decodes .spec to mono 16-bit
  WAV at 32 kHz using IDCT-OLA synthesis (no synthesis window).
  The analysis Hann window at 50% overlap satisfies w[n]+w[n+H]=1,
  so the synthesis window must be rectangular for perfect reconstruction.

- Add imdct_512 / imdct_fft to audio lib (fft.cc, fft.h, idct.cc, dct.h)
  for future MDCT-based synthesis.

- test_wav_roundtrip: in-process OLA analyze+decode SNR test (≥30 dB).
  Currently measures 53 dB on a 440 Hz sine.

- Fix stale test_spectool.cc: version assertion updated from 1 to
  SPEC_VERSION_V2_OLA (was always wrong since OLA fix landed).

- Docs: TOOLS_REFERENCE.md removes dead specview, documents --wav /
  --normalize / test_gen. HOWTO.md adds decode section. TRACKER.md
  notes spec v2 OLA format and decode command.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

3 files changed, 25 insertions, 13 deletions

diff --git a/doc/HOWTO.md b/doc/HOWTO.md
index 768e51d..cc43e7c 100644
--- a/doc/HOWTO.md
+++ b/doc/HOWTO.md
@@ -257,6 +257,17 @@ cmake --build build -j4 --target spectool
 
 Requires `ffmpeg` for `.aif` input files. Output uses v2 format (OLA, Hann, hop=256).
 
+### Decoding .spec to WAV
+
+To verify or inspect a `.spec` file as audio:
+
+```bash
+./build/spectool --wav input.spec output.wav
+```
+
+Produces a mono 16-bit PCM WAV at 32 kHz using IDCT-OLA synthesis (no synthesis window —
+the analysis Hann window is its own reconstruction filter at 50% overlap).
+
 ---
 
 ## Assets
diff --git a/doc/TOOLS_REFERENCE.md b/doc/TOOLS_REFERENCE.md
index 61412a9..f99d213 100644
--- a/doc/TOOLS_REFERENCE.md
+++ b/doc/TOOLS_REFERENCE.md
@@ -26,24 +26,21 @@ Comprehensive reference for all developer tools in the project.
 cmake -S . -B build -DDEMO_BUILD_TOOLS=ON
 cmake --build build -j4
 
-# Analyze WAV → .spec
+# Analyze WAV/MP3 → .spec (v2 OLA format)
 ./build/spectool analyze input.wav output.spec
+./build/spectool analyze input.wav output.spec --normalize        # normalize to RMS 0.15
+./build/spectool analyze input.wav output.spec --normalize 0.20   # custom RMS target
 
-# Play .spec file
-./build/spectool play input.spec
-```
-
----
+# Decode .spec → mono 16-bit WAV (32 kHz, IDCT-OLA synthesis)
+./build/spectool --wav input.spec output.wav
 
-## specview (Visualization)
+# Play .spec file via audio device
+./build/spectool play input.spec
 
-```bash
-# View spectrogram
-./build/specview input.spec
+# Generate test spectrogram (C major scale)
+./build/spectool test_gen output.spec
 ```
 
-Displays spectrogram visualization.
-
 ---
 
 ## specplay (Diagnostic)
diff --git a/doc/TRACKER.md b/doc/TRACKER.md
index 53d8338..e2c21aa 100644
--- a/doc/TRACKER.md
+++ b/doc/TRACKER.md
@@ -24,7 +24,7 @@ HUMANIZE SEED <int> TIMING <pct> VOLUME <pct>  # Optional humanization
 # Generated samples:
 SAMPLE <name>, <freq>, <dur>, <amp>, <attack>, <harmonics>, <decay> [OFFSET <sec>]
 
-# Asset samples (.spec):
+# Asset samples (.spec v2 OLA format — generated by spectool analyze):
 SAMPLE <asset_id> [OFFSET <sec>]         # ASSET_* from assets.txt
 
 # Asset samples (MP3, non-STRIP_ALL only):
@@ -32,6 +32,10 @@ SAMPLE <asset_id> [OFFSET <sec>]         # ASSET_* from assets.txt
 # Add to assets.txt: NAME, NONE, music/file.mp3, "description"
 SAMPLE ASSET_NAME [OFFSET <sec>]         # Decoded at init; same syntax as .spec
 
+# .spec format: SPEC_VERSION_V2_OLA (version=2). Synthesis uses IDCT-OLA
+# (Hann analysis window, 50% overlap, hop=256 samples at 32 kHz).
+# Decode a .spec to WAV for inspection: spectool --wav input.spec out.wav
+
 # Auto-generated notes (no SAMPLE declaration needed):
 # NOTE_C4, NOTE_A#3, NOTE_Eb2, etc.