feat: add FFT-based audio spectrum analyzer module

- Implement radix-2 Cooley-Tukey FFT algorithm
- Add windowing functions: Hann, Hamming, Blackman, Rectangular
- Support configurable frequency bin count
- Add peak detection with configurable decay rate
- Include temporal smoothing for visualization
- Add spectrum analysis example program
- Proper memory management with init/close lifecycle

Bug-fix: Add buffer bounds checking to prevent overflow when sample count is not power of 2
Signed-off-by: Srikanth Patchava <spatchava@meta.com>

examples/audio/audio_spectrum.c

@@ -0,0 +1,126 @@
+/*******************************************************************************************
+*
+*   raylib [audio] example - Audio Spectrum Analyzer
+*
+*   Example originally created with raylib, using raudio_analyzer module
+*
+*   Example licensed under an unmodified zlib/libpng license, which is an OSI-certified,
+*   BSD-like license that allows static linking with closed source software
+*
+*   Copyright (c) 2024 raylib contributors
+*
+********************************************************************************************/
+
+#include "raylib.h"
+#include "../src/raudio_analyzer.h"
+
+#define SCREEN_WIDTH    800
+#define SCREEN_HEIGHT   450
+#define NUM_BARS         64     // Number of frequency bars to draw
+#define FFT_SIZE        512     // FFT bin count (must be power of 2)
+
+int main(void)
+{
+    // Initialization
+    //--------------------------------------------------------------------------
+    InitWindow(SCREEN_WIDTH, SCREEN_HEIGHT, "raylib [audio] example - spectrum analyzer");
+    InitAudioDevice();
+
+    Music music = LoadMusicStream("resources/guitar_noodling.ogg");
+    PlayMusicStream(music);
+
+    // Configure and initialize spectrum analyzer
+    SpectrumConfig config = {
+        .binCount = FFT_SIZE,
+        .windowFunc = WINDOW_HANN,
+        .smoothingFactor = 0.8f,
+        .peakDecayRate = 0.95f,
+        .sampleRate = 44100,
+    };
+    InitSpectrumAnalyzer(config);
+
+    float samples[FFT_SIZE] = { 0 };   // Buffer for audio samples
+
+    SetTargetFPS(60);
+    //--------------------------------------------------------------------------
+
+    // Main game loop
+    while (!WindowShouldClose())
+    {
+        // Update
+        //----------------------------------------------------------------------
+        UpdateMusicStream(music);
+
+        // Feed samples into spectrum analyzer
+        UpdateSpectrum(samples, FFT_SIZE);
+        ApplySmoothing();
+
+        float *spectrum = GetSpectrumData();
+        //----------------------------------------------------------------------
+
+        // Draw
+        //----------------------------------------------------------------------
+        BeginDrawing();
+
+            ClearBackground(RAYWHITE);
+
+            // Draw frequency bars
+            int barWidth = SCREEN_WIDTH / NUM_BARS;
+            int binsPerBar = (FFT_SIZE / 2) / NUM_BARS;
+            if (binsPerBar < 1) binsPerBar = 1;
+
+            for (int i = 0; i < NUM_BARS; i++)
+            {
+                // Average magnitudes across bins for this bar
+                float magnitude = 0.0f;
+                for (int j = 0; j < binsPerBar; j++)
+                {
+                    int binIndex = i * binsPerBar + j;
+                    if (binIndex < FFT_SIZE / 2 && spectrum != NULL)
+                    {
+                        magnitude += spectrum[binIndex];
+                    }
+                }
+                magnitude /= (float)binsPerBar;
+
+                // Scale for visual display
+                int barHeight = (int)(magnitude * SCREEN_HEIGHT * 4.0f);
+                if (barHeight > SCREEN_HEIGHT) barHeight = SCREEN_HEIGHT;
+
+                // Color gradient from green (low) to red (high)
+                Color barColor = (Color){
+                    (unsigned char)(255 * i / NUM_BARS),
+                    (unsigned char)(255 * (NUM_BARS - i) / NUM_BARS),
+                    50,
+                    255
+                };
+
+                DrawRectangle(
+                    i * barWidth,
+                    SCREEN_HEIGHT - barHeight,
+                    barWidth - 2,
+                    barHeight,
+                    barColor
+                );
+            }
+
+            // Display info
+            DrawText("AUDIO SPECTRUM ANALYZER", 10, 10, 20, DARKGRAY);
+            DrawText(TextFormat("Peak Freq: %.1f Hz", GetPeakFrequency()), 10, 40, 16, GRAY);
+            DrawText(TextFormat("Peak Mag:  %.4f", GetPeakMagnitude()), 10, 60, 16, GRAY);
+            DrawFPS(SCREEN_WIDTH - 90, 10);
+
+        EndDrawing();
+        //----------------------------------------------------------------------
+    }
+
+    // De-Initialization
+    //--------------------------------------------------------------------------
+    CloseSpectrumAnalyzer();
+    UnloadMusicStream(music);
+    CloseAudioDevice();
+    CloseWindow();
+    //--------------------------------------------------------------------------
+
+    return 0;
+}