feat(audio): graphic equalizer with presets and custom bands

Adds a 10-band graphic equalizer to AudioSettings (enabled flag +
per-band dB gains, normalised to 10 entries and clamped to range).
Presets return gain curves; the settings page gains EQ UI. libmpv
applies the filter on Linux (Android parity pending). Old persisted
settings without EQ fields load as disabled + flat.

Also includes the requirements/traceability/ux-flows doc updates for
this feature and the home long-press routing (UR-058/DR-087).

TRACES: UR-027 | IR-020, DR-030 | UT-079, UT-080, UT-081, UT-082

src-tauri/src/player/mpv_backend.rs

@@ -3,7 +3,7 @@ use super::events::{PlayerEventEmitter, PlayerStatusEvent};
 use super::media::{MediaItem, MediaSource};
 use super::state::PlayerState;
 use crate::playback_reporting::{EventThrottler, PlaybackOperation, PlaybackReporter};
-use crate::settings::AudioSettings;
+use crate::settings::{AudioSettings, VolumeLevel, EQ_BANDS};
 use crate::utils::conversions::{seconds_to_ticks, volume_to_percent};
 use crate::utils::lock::MutexSafe;
 use libmpv::Mpv;
@@ -552,8 +552,19 @@ impl PlayerBackend for MpvBackend {
                 })?;
         }
 
+        // Audio filter chain: build a single lavfi graph combining the EQ
+        // peaking bands and (optionally) a dynamic loudness normalizer, and
+        // set the `af` property. An empty string clears all filters. Both
+        // features share one `af` graph because MPV exposes a single filter
+        // property. See docs/specs/audio-equalizer.md and IR-020.
+        let af = build_af_filter(settings);
+        self.mpv
+            .set_property("af", af.as_str())
+            .map_err(|e| PlayerError {
+                message: format!("Failed to set audio filters: {:?}", e),
+            })?;
+
         // TODO: Implement crossfade via MPV audio filters if needed
-        // TODO: Implement volume normalization if needed
 
         Ok(())
     }
@@ -563,9 +574,200 @@ impl PlayerBackend for MpvBackend {
     }
 }
 
+/// Build the full MPV `af` (audio filter) value from the audio settings.
+///
+/// Combines the equalizer peaking bands and the loudness-normalization filter
+/// into a single `lavfi` graph, because MPV exposes one `af` property. The
+/// normalizer runs *after* the EQ so it levels the post-EQ signal. Returns an
+/// empty string when neither feature contributes a filter, which clears `af`.
+///
+/// TRACES: UR-027, UR-033 | IR-020, DR-036
+fn build_af_filter(settings: &AudioSettings) -> String {
+    let mut entries = eq_filter_entries(settings.equalizer_enabled, &settings.equalizer_bands);
+    if let Some(norm) = normalize_filter_entry(settings.normalize_volume, settings.volume_level) {
+        entries.push(norm);
+    }
+
+    if entries.is_empty() {
+        return String::new();
+    }
+    format!("lavfi=[{}]", entries.join(","))
+}
+
+/// Peaking-EQ filter entries (unwrapped), one ffmpeg `equalizer` (two-pole
+/// peaking) per band with a non-zero gain, e.g.
+/// `equalizer=f=31:width_type=o:width=1:g=5`. Returns an empty vec when the EQ
+/// is disabled or every gain is ~0. Gains are assumed already normalised by
+/// [`AudioSettings::with_equalizer_normalised`]; bands beyond [`EQ_BANDS`] are
+/// ignored.
+///
+/// TRACES: UR-027 | IR-020
+fn eq_filter_entries(enabled: bool, bands: &[f32]) -> Vec<String> {
+    if !enabled {
+        return Vec::new();
+    }
+    bands
+        .iter()
+        .zip(EQ_BANDS.iter())
+        .filter(|(gain, _)| gain.abs() >= 0.05) // skip ~0 dB bands
+        .map(|(gain, freq)| {
+            // width_type=o → octave bandwidth; width=1 → one octave per band.
+            format!("equalizer=f={}:width_type=o:width=1:g={}", freq, gain)
+        })
+        .collect()
+}
+
+/// Reference peak (`dynaudnorm` `p`, linear amplitude) for the default
+/// [`VolumeLevel::Normal`] (−14 LUFS) target, leaving −1.2 dB of headroom.
+const NORMALIZE_REF_PEAK: f32 = 0.87;
+/// Reference loudness the peak table is anchored at (Normal preset, −14 LUFS).
+const NORMALIZE_REF_LUFS: f32 = -14.0;
+
+/// The loudness-normalization filter entry (unwrapped), or `None` when
+/// normalization is disabled. Uses ffmpeg's `dynaudnorm`, a gentle real-time
+/// dynamic normalizer that avoids the gain "pumping" `loudnorm`'s single-pass
+/// mode can produce on very dynamic material.
+///
+/// `dynaudnorm` targets a peak amplitude (`p`, linear 0–1), not a LUFS value,
+/// so the Loud/Normal/Quiet presets become *approximate*: each preset's LUFS
+/// offset from the Normal reference is applied as a dB offset to the reference
+/// peak, preserving the Loud > Normal > Quiet ordering. `g=15` (gaussian window
+/// size) further smooths gain changes; the peak is clamped to a safe (0, 0.99]
+/// so loud presets never request full-scale.
+///
+/// TRACES: UR-033 | DR-036
+fn normalize_filter_entry(enabled: bool, level: VolumeLevel) -> Option<String> {
+    if !enabled {
+        return None;
+    }
+    // LUFS above the reference → louder → higher peak; each +1 LUFS ≈ +1 dB.
+    let db_offset = level.target_lufs() - NORMALIZE_REF_LUFS;
+    let peak = (NORMALIZE_REF_PEAK * 10f32.powf(db_offset / 20.0)).clamp(0.10, 0.99);
+    // 3 decimals is plenty for a peak target and keeps the filter string stable.
+    Some(format!("dynaudnorm=p={:.3}:g=15", peak))
+}
+
 impl Drop for MpvBackend {
     fn drop(&mut self) {
         info!("[MpvBackend] Shutting down");
         // MPV will be automatically cleaned up
     }
 }
+
+#[cfg(test)]
+mod af_filter_tests {
+    use super::{build_af_filter, eq_filter_entries, normalize_filter_entry};
+    use crate::settings::{AudioSettings, VolumeLevel};
+
+    fn settings() -> AudioSettings {
+        AudioSettings {
+            equalizer_enabled: false,
+            equalizer_bands: vec![0.0; 10],
+            normalize_volume: false,
+            ..AudioSettings::default()
+        }
+    }
+
+    /// Disabled EQ, or an all-zero curve, produces no EQ entries.
+    ///
+    /// TRACES: UR-027 | IR-020 | UT-083
+    #[test]
+    fn test_eq_entries_empty_when_disabled_or_flat() {
+        assert!(eq_filter_entries(false, &[5.0, -3.0, 2.0]).is_empty());
+        assert!(eq_filter_entries(true, &[0.0; 10]).is_empty());
+        // Sub-threshold gains count as flat.
+        assert!(eq_filter_entries(true, &[0.01, -0.02]).is_empty());
+    }
+
+    /// Enabled EQ builds one peaking `equalizer` per non-zero band at the right
+    /// centre frequency and gain, chained inside a single `lavfi` filter.
+    ///
+    /// TRACES: UR-027 | IR-020 | UT-084
+    #[test]
+    fn test_eq_filter_builds_lavfi_chain() {
+        // First band (31 Hz) +5 dB, third band (125 Hz) -2 dB, rest flat.
+        let mut s = settings();
+        s.equalizer_enabled = true;
+        s.equalizer_bands = vec![5.0, 0.0, -2.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0];
+        let af = build_af_filter(&s);
+        assert!(af.starts_with("lavfi=["), "wrapped in lavfi: {af}");
+        assert!(af.ends_with("]"));
+        assert!(af.contains("equalizer=f=31:width_type=o:width=1:g=5"));
+        assert!(af.contains("equalizer=f=125:width_type=o:width=1:g=-2"));
+        // Only two bands are non-zero → exactly two peaking filters.
+        assert_eq!(af.matches("equalizer=").count(), 2);
+    }
+
+    /// Disabled normalization yields no filter entry; the combined `af` for a
+    /// fully default (all-off) settings is empty, which clears `af`.
+    ///
+    /// TRACES: UR-033 | DR-036 | UT-085
+    #[test]
+    fn test_normalize_disabled_produces_no_filter() {
+        assert!(normalize_filter_entry(false, VolumeLevel::Normal).is_none());
+        assert_eq!(build_af_filter(&settings()), "");
+    }
+
+    /// Enabled normalization emits a `dynaudnorm` filter with a peak target, and
+    /// the peak preserves the Loud > Normal > Quiet ordering.
+    ///
+    /// TRACES: UR-033 | DR-036 | UT-086
+    #[test]
+    fn test_normalize_peak_preserves_preset_ordering() {
+        fn peak_of(entry: &str) -> f32 {
+            // "dynaudnorm=p=0.870:g=15" → 0.870
+            entry
+                .split("p=")
+                .nth(1)
+                .and_then(|s| s.split(':').next())
+                .and_then(|s| s.parse().ok())
+                .expect("parseable peak")
+        }
+
+        let loud = normalize_filter_entry(true, VolumeLevel::Loud).unwrap();
+        let normal = normalize_filter_entry(true, VolumeLevel::Normal).unwrap();
+        let quiet = normalize_filter_entry(true, VolumeLevel::Quiet).unwrap();
+        for entry in [&loud, &normal, &quiet] {
+            assert!(
+                entry.starts_with("dynaudnorm="),
+                "dynaudnorm filter: {entry}"
+            );
+        }
+        assert!(
+            peak_of(&loud) > peak_of(&normal) && peak_of(&normal) > peak_of(&quiet),
+            "Loud {} > Normal {} > Quiet {}",
+            peak_of(&loud),
+            peak_of(&normal),
+            peak_of(&quiet),
+        );
+        // Every preset stays within the safe (0, 0.99] clamp.
+        for p in [peak_of(&loud), peak_of(&normal), peak_of(&quiet)] {
+            assert!(p > 0.0 && p <= 0.99, "peak in range: {p}");
+        }
+
+        let mut s = settings();
+        s.normalize_volume = true;
+        s.volume_level = VolumeLevel::Quiet;
+        let af = build_af_filter(&s);
+        assert!(af.starts_with("lavfi=["));
+        assert!(af.contains("dynaudnorm=p="));
+    }
+
+    /// EQ and normalization coexist in one `lavfi` graph, with the normalizer
+    /// placed after the EQ bands so it levels the post-EQ signal.
+    ///
+    /// TRACES: UR-027, UR-033 | IR-020, DR-036 | UT-087
+    #[test]
+    fn test_eq_and_normalize_combine_in_order() {
+        let mut s = settings();
+        s.equalizer_enabled = true;
+        s.equalizer_bands = vec![5.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0];
+        s.normalize_volume = true;
+        s.volume_level = VolumeLevel::Normal;
+        let af = build_af_filter(&s);
+
+        let eq_pos = af.find("equalizer=").expect("has EQ");
+        let norm_pos = af.find("dynaudnorm=").expect("has normalizer");
+        assert!(eq_pos < norm_pos, "normalizer runs after EQ: {af}");
+    }
+}