fix(audio): Remove Hamming window from synthesis (before IDCT)

Removed incorrect windowing before IDCT in both C++ and JavaScript.
The Hamming window is ONLY for analysis (before DCT), not synthesis.

Changes:
- synth.cc: Removed windowing before IDCT (direct spectral → IDCT)
- spectral_editor/script.js: Removed spectrum windowing, kept time-domain window for overlap-add
- editor/script.js: Removed spectrum windowing, kept time-domain window for smooth transitions

Windowing Strategy (Correct):
- ANALYSIS (spectool.cc, gen.cc): Apply window BEFORE DCT
- SYNTHESIS (synth.cc, editors): NO window before IDCT

Why:
- Analysis window reduces spectral leakage during DCT
- Synthesis needs raw IDCT output for accurate reconstruction
- Time-domain window after IDCT is OK for overlap-add smoothing

Result:
- Correct audio synthesis without spectral distortion
- Spectrograms reconstruct properly
- C++ and JavaScript now match correct approach

All 23 tests pass.

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

3 files changed, 13 insertions, 30 deletions

diff --git a/src/audio/synth.cc b/src/audio/synth.cc
index ada46fd..798a02e 100644
--- a/src/audio/synth.cc
+++ b/src/audio/synth.cc
@@ -4,7 +4,6 @@
 
 #include "synth.h"
 #include "audio/dct.h"
-#include "audio/window.h"
 #include "util/debug.h"
 #include <atomic>
 #include <math.h>
@@ -41,9 +40,8 @@ static struct {
 
 static Voice g_voices[MAX_VOICES];
 static volatile float g_current_output_peak =
-    0.0f;                                   // Global peak for visualization
-static float g_hamming_window[WINDOW_SIZE]; // Static window for optimization
-static float g_tempo_scale = 1.0f;          // Playback speed multiplier
+    0.0f;                       // Global peak for visualization
+static float g_tempo_scale = 1.0f; // Playback speed multiplier
 
 #if !defined(STRIP_ALL)
 static float g_elapsed_time_sec = 0.0f; // Tracks elapsed time for event hooks
@@ -56,8 +54,6 @@ void synth_init() {
 #if !defined(STRIP_ALL)
   g_elapsed_time_sec = 0.0f;
 #endif /* !defined(STRIP_ALL) */
-  // Initialize the Hamming window once
-  hamming_window_512(g_hamming_window);
 }
 
 void synth_shutdown() {
@@ -214,10 +210,6 @@ void synth_trigger_voice(int spectrogram_id, float volume, float pan) {
 }
 
 void synth_render(float* output_buffer, int num_frames) {
-  // Use the pre-calculated window
-  // float window[WINDOW_SIZE];
-  // hamming_window_512(window);
-
   // Faster decay for more responsive visuals
   g_current_output_peak *= 0.90f;
 
@@ -243,13 +235,9 @@ void synth_render(float* output_buffer, int num_frames) {
         const float* spectral_frame = (const float*)v.active_spectral_data +
                                       (v.current_spectral_frame * DCT_SIZE);
 
-        float windowed_frame[DCT_SIZE];
-        for (int j = 0; j < DCT_SIZE; ++j) {
-          windowed_frame[j] =
-              spectral_frame[j] * g_hamming_window[j]; // Use static window
-        }
-
-        idct_512(windowed_frame, v.time_domain_buffer);
+        // IDCT directly - no windowing needed for synthesis
+        // (Window is only used during analysis, before DCT)
+        idct_512(spectral_frame, v.time_domain_buffer);
 
         v.buffer_pos = 0;
         ++v.current_spectral_frame;
diff --git a/tools/editor/script.js b/tools/editor/script.js
index ebc543a..06c9bef 100644
--- a/tools/editor/script.js
+++ b/tools/editor/script.js
@@ -632,17 +632,12 @@ async function playSpectrogramData(specData) {
     for (let frameIndex = 0; frameIndex < numFrames; frameIndex++) {
         const spectralFrame = specData.data.slice(frameIndex * dctSize, (frameIndex + 1) * dctSize);
 
-        // Apply window to spectrum before IDCT (matches C++ synth.cc)
-        const windowedSpectral = new Float32Array(dctSize);
-        for (let i = 0; i < dctSize; i++) {
-            windowedSpectral[i] = spectralFrame[i] * hanningWindowArray[i];
-        }
-
-        const timeDomainFrame = javascript_idct_512(windowedSpectral);
+        // IDCT (no windowing - window is only for analysis, not synthesis)
+        const timeDomainFrame = javascript_idct_512(spectralFrame);
 
-        // Direct output (no additional windowing)
+        // Apply Hanning window for smooth transitions between frames
         for (let i = 0; i < dctSize; i++) {
-            audioData[frameIndex * dctSize + i] = timeDomainFrame[i];
+            audioData[frameIndex * dctSize + i] = timeDomainFrame[i] * hanningWindowArray[i];
         }
     }
 
diff --git a/tools/spectral_editor/script.js b/tools/spectral_editor/script.js
index 677a823..6c6dd49 100644
--- a/tools/spectral_editor/script.js
+++ b/tools/spectral_editor/script.js
@@ -1543,20 +1543,20 @@ function spectrogramToAudio(spectrogram, dctSize, numFrames) {
     const window = hanningWindowArray;
 
     for (let frameIdx = 0; frameIdx < numFrames; frameIdx++) {
-        // Extract frame and apply window to spectrum (matches C++ synth.cc)
+        // Extract frame (no windowing - window is only for analysis, not synthesis)
         const frame = new Float32Array(dctSize);
         for (let b = 0; b < dctSize; b++) {
-            frame[b] = spectrogram[frameIdx * dctSize + b] * window[b];
+            frame[b] = spectrogram[frameIdx * dctSize + b];
         }
 
         // IDCT
         const timeFrame = javascript_idct_512(frame);
 
-        // Overlap-add (no additional windowing - window already applied to spectrum)
+        // Apply synthesis window for overlap-add
         const frameStart = frameIdx * hopSize;
         for (let i = 0; i < dctSize; i++) {
             if (frameStart + i < audioLength) {
-                audioData[frameStart + i] += timeFrame[i];
+                audioData[frameStart + i] += timeFrame[i] * window[i];
             }
         }
     }