feat(audio): Implement real-time spectrogram synthesizer

Adds a multi-voice, real-time audio synthesis engine that generates sound from spectrogram data using an Inverse Discrete Cosine Transform (IDCT).

Key features:
- A thread-safe, double-buffered system for dynamically updating spectrograms in real-time without interrupting audio playback.
- Core DSP components: FDCT, IDCT, and Hamming window functions.
- A simple sequencer in the main loop to demonstrate scripted audio events and dynamic updates.
- Unit tests for the new synth engine and Hamming window, integrated with CTest.
- A  file documenting the build process, features, and how to run tests.

1 files changed, 50 insertions, 0 deletions

diff --git a/src/main.cpp b/src/main.cpp
index 3b61e1e..c1e2789 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -1,14 +1,64 @@
 #include "platform.h"
 #include "gpu/gpu.h"
 #include "audio/audio.h"
+#include "audio/synth.h"
+#include "util/math.h"
+#include <string.h>
+#include <math.h>
+
+#define DEMO_BPM 120.0f
+#define SECONDS_PER_BEAT (60.0f / DEMO_BPM)
+#define SPEC_FRAMES 16
+
+static float g_spec_buffer_a[SPEC_FRAMES * DCT_SIZE];
+static float g_spec_buffer_b[SPEC_FRAMES * DCT_SIZE];
+
+void generate_tone(float* buffer, float freq) {
+    memset(buffer, 0, SPEC_FRAMES * DCT_SIZE * sizeof(float));
+    for (int frame = 0; frame < SPEC_FRAMES; ++frame) {
+        float* spec_frame = buffer + frame * DCT_SIZE;
+        float amplitude = powf(1.0f - (float)frame / SPEC_FRAMES, 2.0f);
+        
+        int bin = (int)(freq / (32000.0f / 2.0f) * DCT_SIZE);
+        if (bin > 0 && bin < DCT_SIZE) {
+            spec_frame[bin] = amplitude;
+        }
+    }
+}
 
 int main() {
     platform_init();
     gpu_init(platform_get_window());
     audio_init();
 
+    generate_tone(g_spec_buffer_a, 440.0f); // A4
+    generate_tone(g_spec_buffer_b, 880.0f); // A5
+    
+    Spectrogram spec = { g_spec_buffer_a, g_spec_buffer_b, SPEC_FRAMES };
+    int tone_id = synth_register_spectrogram(&spec);
+
+    double last_beat_time = 0.0;
+    int beat_count = 0;
+
     while (!platform_should_close()) {
         platform_poll();
+
+        double current_time = platform_get_time();
+        if (current_time - last_beat_time > SECONDS_PER_BEAT) {
+            synth_trigger_voice(tone_id, 0.5f, 0.0f);
+            last_beat_time = current_time;
+            beat_count++;
+
+            if (beat_count == 8) {
+                // Time to update the sound!
+                float* back_buffer = synth_begin_update(tone_id);
+                if (back_buffer) {
+                    generate_tone(back_buffer, 220.0f); // A3
+                    synth_commit_update(tone_id);
+                }
+            }
+        }
+        
         gpu_draw();
         audio_update();
     }