perf(analysis): reuse sorted spectral percentile windows

Reuse sorted windows for related percentiles and reject unsuitable edges before computing expensive tail statistics. Preserve cutoff results with 31 regression fixtures and 400 exact old/new comparisons.

test/audio_analysis_spectrogram_test.dart

@@ -222,6 +222,58 @@ lavfi.r128.true_peak=0.907
     const height = 800;
     const nyquist = 96000.0;
 
+    test('preserves exact cutoffs across noisy and transient spectra', () {
+      // Captured from the estimator before sharing sorted percentile windows.
+      // Cover sharp/gradual limits, full-band slopes, noise and stepped bands
+      // at several resolutions and Nyquist frequencies.
+      const expected = <int, double>{
+        3: 5290.322580645161,
+        7: 5406.25,
+        11: 5403.508771929824,
+        15: 5395.0,
+        31: 14952.65625,
+        47: 16305.0,
+        63: 32610.0,
+        79: 65220.0,
+        83: 5032.258064516129,
+        87: 5156.25,
+        91: 5162.907268170426,
+        95: 5155.0,
+        111: 14291.15625,
+        127: 15585.0,
+        143: 31230.0,
+        159: 62340.0,
+        175: 8000.0,
+        191: 22050.0,
+        207: 24000.0,
+        223: 48000.0,
+        239: 96000.0,
+        255: 8000.0,
+        271: 22050.0,
+        287: 24000.0,
+        303: 48000.0,
+        319: 96000.0,
+        335: 5795.0,
+        351: 16055.15625,
+        367: 17505.0,
+        383: 35010.0,
+        399: 70020.0,
+      };
+      for (final entry in expected.entries) {
+        final spectrum = _noisySpectrum(entry.key);
+        expect(
+          estimateEffectiveSpectralCutoffHz(
+            intensity: spectrum.intensity,
+            width: spectrum.width,
+            height: spectrum.height,
+            maxFrequencyHz: spectrum.maxFrequencyHz,
+          ),
+          entry.value,
+          reason: 'spectrum ${entry.key}',
+        );
+      }
+    });
+
     test('ignores a narrow ultrasonic pilot above a 22 kHz music band', () {
       final intensity = _blankIntensity(width, height, value: 12);
       _paintFrequencyBand(
@@ -585,6 +637,51 @@ lavfi.r128.true_peak=0.907
   });
 }
 
+({Uint8List intensity, int width, int height, double maxFrequencyHz})
+_noisySpectrum(int seed) {
+  final width = [17, 83, 200, 400][seed % 4];
+  final height = [31, 128, 399, 800][(seed ~/ 4) % 4];
+  final maxFrequencyHz = [
+    8000.0,
+    22050.0,
+    24000.0,
+    48000.0,
+    96000.0,
+  ][(seed ~/ 16) % 5];
+  final intensity = Uint8List(width * height);
+  var random = seed + 1;
+  final mode = (seed ~/ 80) % 5;
+  for (var y = 0; y < height; y++) {
+    final frequency = (height - y - 1) / (height - 1);
+    for (var x = 0; x < width; x++) {
+      random = (1664525 * random + 1013904223) & 0xffffffff;
+      final noise = (random >> 24) % 13;
+      final base = switch (mode) {
+        0 => frequency < 0.68 ? 120 : 24,
+        1 => frequency < 0.65 ? (160 - frequency * 170).round() : 24,
+        2 => (140 - frequency * 110).round(),
+        3 => 16 + (random >> 20) % 170,
+        _ =>
+          frequency < 0.35
+              ? 90
+              : frequency < 0.73
+              ? 64
+              : 35,
+      };
+      // Five percent broadband transients remain below the temporal P90.
+      intensity[y * width + x] = x < width ~/ 20
+          ? 255
+          : (base + noise).clamp(0, 255);
+    }
+  }
+  return (
+    intensity: intensity,
+    width: width,
+    height: height,
+    maxFrequencyHz: maxFrequencyHz,
+  );
+}
+
 Uint8List _blankIntensity(int width, int height, {int value = 0}) {
   final intensity = Uint8List(width * height);
   if (value > 0) intensity.fillRange(0, intensity.length, value);