fix(analysis): detect full-band spectral cutoff

test/audio_analysis_info_card_test.dart

@@ -0,0 +1,26 @@
+import 'package:flutter_test/flutter_test.dart';
+import 'package:spotiflac_android/widgets/audio_analysis_widget.dart';
+
+void main() {
+  group('spectral cutoff formatting', () {
+    test('formats a detected cutoff frequency', () {
+      expect(
+        formatAudioAnalysisSpectralCutoff(
+          22605,
+          notDetectedLabel: 'Not detected',
+        ),
+        '22.6 kHz',
+      );
+    });
+
+    test('keeps the metric visible when no cutoff is detected', () {
+      expect(
+        formatAudioAnalysisSpectralCutoff(
+          null,
+          notDetectedLabel: 'Not detected',
+        ),
+        'Not detected',
+      );
+    });
+  });
+}

test/audio_analysis_spectrogram_test.dart

@@ -250,6 +250,30 @@ lavfi.r128.true_peak=0.907
       expect(cutoff, nyquist);
     });
 
+    test(
+      'reports Nyquist for full-band music with a natural spectral tilt',
+      () {
+        const cdNyquist = 22050.0;
+        final intensity = _blankIntensity(width, height);
+        _paintNaturalSpectralTilt(
+          intensity,
+          width: width,
+          height: height,
+          lowFrequencyIntensity: 140,
+          nyquistIntensity: 26,
+        );
+
+        final cutoff = estimateEffectiveSpectralCutoffHz(
+          intensity: intensity,
+          width: width,
+          height: height,
+          maxFrequencyHz: cdNyquist,
+        );
+
+        expect(cutoff, cdNyquist);
+      },
+    );
+
     test('does not report an isolated line as a broadband cutoff', () {
       final intensity = _blankIntensity(width, height);
       _paintFrequencyBand(
@@ -312,3 +336,24 @@ void _paintFrequencyBand(
     }
   }
 }
+
+void _paintNaturalSpectralTilt(
+  Uint8List values, {
+  required int width,
+  required int height,
+  required int lowFrequencyIntensity,
+  required int nyquistIntensity,
+}) {
+  final span = lowFrequencyIntensity - nyquistIntensity;
+  for (var y = 0; y < height; y++) {
+    final normalizedFrequency = (height - y - 0.5) / height;
+    final intensity =
+        (lowFrequencyIntensity -
+                span * normalizedFrequency * normalizedFrequency)
+            .round()
+            .clamp(0, 255);
+    for (var x = 0; x < width; x++) {
+      values[y * width + x] = intensity;
+    }
+  }
+}