fix(audio): correct OLA synthesis and extract shared ola_encode/ola_decode

- Remove erroneous Hann synthesis window from synth.cc (g_hann * tmp[j]).
  Hann analysis at 50% overlap satisfies w[n]+w[n+H]=1, so rectangular
  synthesis gives perfect reconstruction; applying Hann twice was wrong.
- Extract ola_encode()/ola_decode()/ola_num_frames() into src/audio/ola.h+cc.
  spectool and test_wav_roundtrip now use the shared functions.
  synth.cc lazy-decode path stays inlined (see TODO for future refactor).
- Drop dead <atomic> include and g_hann array from synth.cc.
- Drop dead window.h include from spectool.cc.
- Update PROJECT_CONTEXT.md, COMPLETED.md, TODO.md to reflect correct
  analysis-only Hann window and new ola.h API.

handoff(Gemini): OLA synthesis bug fixed + ola.h factorized. synth.cc
lazy-decode still inline (TODO item added). 34/35 tests pass; WavDumpBackendTest
failure is pre-existing and unrelated.

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

1 files changed, 9 insertions, 51 deletions

diff --git a/src/tests/audio/test_wav_roundtrip.cc b/src/tests/audio/test_wav_roundtrip.cc
index 6294d6d..79de6ad 100644
--- a/src/tests/audio/test_wav_roundtrip.cc
+++ b/src/tests/audio/test_wav_roundtrip.cc
@@ -1,9 +1,8 @@
 // Tests the wav->spec->wav roundtrip SNR.
-// Generates a sine wave, runs OLA-DCT analysis then IMDCT-OLA synthesis,
+// Generates a sine wave, runs OLA encode then OLA decode,
 // and asserts the reconstruction SNR exceeds the threshold.
 
-#include "audio/dct.h"
-#include "audio/window.h"
+#include "audio/ola.h"
 #include <assert.h>
 #include <cmath>
 #include <cstdio>
@@ -12,49 +11,6 @@
 static const int SAMPLE_RATE = 32000;
 static const float PI = 3.14159265358979323846f;
 
-// Replicate analyze_audio OLA pass (Hann + FDCT, hop = OLA_HOP_SIZE)
-static std::vector<float> ola_analyze(const std::vector<float>& pcm) {
-  float win[DCT_SIZE];
-  hann_window_512(win);
-
-  const int hop = OLA_HOP_SIZE;
-  const int n_pcm = (int)pcm.size();
-  const int num_frames = (n_pcm > DCT_SIZE) ? (n_pcm - DCT_SIZE) / hop + 1 : 1;
-
-  std::vector<float> spec(num_frames * DCT_SIZE);
-  float chunk[DCT_SIZE];
-
-  for (int f = 0; f < num_frames; ++f) {
-    const int start = f * hop;
-    const int avail = (start + DCT_SIZE <= n_pcm) ? DCT_SIZE : n_pcm - start;
-    for (int i = 0; i < avail; ++i) chunk[i] = pcm[start + i] * win[i];
-    for (int i = avail; i < DCT_SIZE; ++i) chunk[i] = 0.0f;
-
-    fdct_512(chunk, spec.data() + f * DCT_SIZE);
-  }
-  return spec;
-}
-
-// IDCT + OLA synthesis (no synthesis window) matching decode_to_wav.
-// Analysis used Hann; since Hann satisfies w[n]+w[n+H]=1 at 50% overlap,
-// skipping the synthesis window gives perfect reconstruction.
-static std::vector<float> ola_decode(const std::vector<float>& spec,
-                                     int num_frames) {
-  std::vector<float> pcm(num_frames * OLA_HOP_SIZE + OLA_OVERLAP, 0.0f);
-  float overlap[OLA_OVERLAP] = {};
-  float tmp[DCT_SIZE];
-
-  for (int f = 0; f < num_frames; ++f) {
-    idct_512(spec.data() + f * DCT_SIZE, tmp);
-    for (int j = 0; j < OLA_HOP_SIZE; ++j)
-      pcm[f * OLA_HOP_SIZE + j] = tmp[j] + overlap[j];
-    for (int j = 0; j < OLA_OVERLAP; ++j)
-      overlap[j] = tmp[OLA_HOP_SIZE + j];
-  }
-  pcm.resize(num_frames * OLA_HOP_SIZE);
-  return pcm;
-}
-
 static float compute_snr_db(const std::vector<float>& ref,
                              const std::vector<float>& out,
                              int skip_samples) {
@@ -78,12 +34,14 @@ int main() {
   for (int i = 0; i < n_samples; ++i)
     input[i] = 0.5f * sinf(2.0f * PI * 440.0f * i / SAMPLE_RATE);
 
-  // Analyze
-  std::vector<float> spec = ola_analyze(input);
-  const int num_frames = (int)(spec.size() / DCT_SIZE);
+  // Encode
+  const int num_frames = ola_num_frames(n_samples);
+  std::vector<float> spec(num_frames * DCT_SIZE);
+  ola_encode(input.data(), n_samples, spec.data(), num_frames);
 
-  // Decode with IDCT-OLA (no synthesis window)
-  std::vector<float> output = ola_decode(spec, num_frames);
+  // Decode
+  std::vector<float> output(num_frames * OLA_HOP_SIZE);
+  ola_decode(spec.data(), num_frames, output.data());
 
   // SNR — skip first DCT_SIZE samples (ramp-up transient)
   const float snr = compute_snr_db(input, output, DCT_SIZE);