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# Design: enterprise-audio-analysis-loudness
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**Change ID**: enterprise-audio-analysis-loudness
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**Package**: `@suaveplan/audio-analysis-loudness`
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`@suaveplan/audio-analysis-loudness` is a leaf analysis plugin in the `@suaveplan/audio-*` family.
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It measures loudness — integrated/short-term/momentary LUFS, loudness range, true peak, RMS, sample
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peak, and per-channel DC offset — for broadcast-compliance, mastering, and auto-normalization
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pipelines. This document carries the **package-specific design**; the cross-cutting audio
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ecosystem architecture is not duplicated here.
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---
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## 1. Relationship to the audio ecosystem
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The cross-cutting architecture for the whole `@suaveplan/audio-*` family lives in
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`enterprise-audio-core/design.md` §1–§4 — the three-layer separation, the six plugin slots, the
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zero-duplication rule for genesis primitives, and the `AudioError` hierarchy. This package does not
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restate that model; it references it.
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`LoudnessMeter` occupies **plugin slot 3 — Analysis Op** (`enterprise-audio-core/design.md` §1.3).
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Analysis ops are *sidecar* processors: they read an `AudioDocument` and emit features, and they are
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**not** part of the render pipeline. The meter never registers a plan op or a process op; it
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consumes audio through `@suaveplan/audio-core`'s read/stream APIs and returns a `LoudnessResult`.
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The `AnalysisOp` and `AnalysisResult` interfaces are defined by `@suaveplan/audio-core`. This
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package implements `AnalysisOp` and extends `AnalysisResult` into `LoudnessResult`.
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---
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## 2. Algorithm rationale
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### 2.1. K-weighting filter (ITU-R BS.1770)
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BS.1770 loudness is *not* raw RMS — it is the energy of a **K-weighted** signal. The K-weighting
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curve is a two-stage IIR cascade applied per channel before any energy is accumulated:
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- **Stage 1 — high-shelf "pre-filter".** A second-order shelving biquad that models the acoustic
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effect of the listener's head, boosting high frequencies by roughly +4 dB.
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- **Stage 2 — RLB high-pass.** A second-order Butterworth-style high-pass (the "revised
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low-frequency B-curve") that rolls off content below ~100 Hz so sub-bass rumble does not
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dominate the measurement.
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Coefficients are sample-rate dependent. The canonical BS.1770 coefficients are specified at
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48 kHz; for other rates (notably 44.1 kHz) the analog prototype is re-discretised via the bilinear
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transform so the magnitude response matches. The filter keeps per-channel biquad state
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(`z1`, `z2` per stage) so it can be driven incrementally over streamed blocks and still produce
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output sample-identical to a single whole-buffer pass.
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```ts
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interface Biquad {
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b0: number; b1: number; b2: number; a1: number; a2: number
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}
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interface KWeightingState {
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pre: Float64Array // [z1, z2] per channel for stage 1
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rlb: Float64Array // [z1, z2] per channel for stage 2
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}
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function buildKWeighting(sampleRate: number): { pre: Biquad; rlb: Biquad }
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function filterBlock(block: Float32Array[], coeffs, state: KWeightingState): Float32Array[]
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```
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### 2.2. Gating (BS.1770-4)
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Integrated loudness is a *gated* mean of K-weighted energy, not a simple average:
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1. Energy is accumulated over **400 ms gating blocks** that **overlap by 75%** (a new block every
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100 ms).
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2. Each block's per-channel mean square is summed with the BS.1770 **channel weights** (1.0 for L,
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R, C; 1.41 for the surround channels) to a single loudness value.
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3. The **absolute gate** discards every block below **−70 LUFS** — this removes silence and
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near-silence.
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4. The ungated mean of the survivors sets a **relative gate** at **−10 LU** below it; blocks below
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the relative gate are discarded.
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5. Integrated loudness is the loudness of the mean energy of the doubly-gated survivor set.
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Momentary loudness uses the same K-weighting and channel-summing over a single ungated **400 ms**
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window; short-term loudness over a **3 s** window. These feed `analyzeBlock` (momentary) and the
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loudness-range computation (short-term).
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### 2.3. Loudness range — EBU Tech 3342
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`loudnessRange` (LRA, in LU) is a statistical measure of dynamic spread:
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1. Collect **short-term** loudness over 3 s windows stepped by 1 s.
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2. Apply an absolute gate at −70 LUFS, then a relative gate **20 LU** below the gated mean (note:
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wider than the integrated-loudness relative gate of 10 LU — this is intentional in Tech 3342).
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3. LRA is the **95th percentile minus the 10th percentile** of the surviving distribution.
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A document shorter than one 3 s window cannot produce a distribution, so LRA is reported as `0`.
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### 2.4. True-peak — 4x oversampling (BS.1770-4 Annex 2)
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Sample peak under-reports the real analog peak because the true waveform crests *between* samples.
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BS.1770-4 specifies **4x oversampling** through a polyphase FIR interpolation filter; `truePeak`
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(dBTP) is the maximum absolute interpolated sample across all channels. By construction
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`truePeak >= peak` always — the original samples are a subset of the interpolated set.
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```ts
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// 4-phase polyphase FIR; each phase is a short symmetric low-pass kernel.
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function truePeakDbtp(block: Float32Array[]): number
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```
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### 2.5. RMS, peak, DC offset
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`rms` is `20 * log10(sqrt(meanSquare))` across all channels; `peak` is
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`20 * log10(maxAbsSample)`; `dcOffset[c]` is the arithmetic mean of channel `c`. For digital
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silence, `rms` and `lufs` are clamped to finite BS.1770 floor values rather than `-Infinity`, so
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downstream consumers (normalizers, UI meters) never have to special-case `-Infinity`.
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---
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## 3. Public surface and result shape
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```ts
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interface LoudnessMeterOptions {
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blockSize?: number // gating block length in ms; default 400 (BS.1770)
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overlap?: number // gating overlap fraction 0..1; default 0.75
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targetLufs?: number // reference target; default -14.0 (streaming), -23.0 (broadcast)
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signal?: AbortSignal // cooperative cancellation for analyze / analyzeStream
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}
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interface LoudnessResult extends AnalysisResult {
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lufs: number // integrated loudness (LUFS)
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loudnessRange: number // LRA (LU)
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truePeak: number // dBTP
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rms: number // dB
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peak: number // dB
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dcOffset: number[] // per-channel mean sample value
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}
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class LoudnessMeter implements AnalysisOp {
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readonly name = 'loudness-meter'
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readonly description = 'ITU-R BS.1770-4 loudness measurement'
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constructor(options?: LoudnessMeterOptions)
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analyze(doc: AudioDocument, opts?: LoudnessMeterOptions): Promise<LoudnessResult>
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analyzeStream(doc: AudioDocument, opts?: LoudnessMeterOptions): AsyncGenerator<LoudnessResult>
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analyzeBlock(block: Float32Array[], ctx: BlockContext): Partial<LoudnessResult>
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}
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```
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`analyze` and `analyzeStream` share one gating engine: `analyze` drains the document and runs the
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engine to completion; `analyzeStream` yields the engine's running integrated loudness after every
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gating block. The invariant is that the final `analyzeStream` yield equals the `analyze` result
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for the same document — the streaming path is the batch path observed incrementally, not a
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separate approximation.
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`analyzeBlock` is the real-time path: synchronous, allocation-light (it reuses a per-instance
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scratch filter state), and safe to call on every audio callback for live meters. It returns only
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the per-block fields it can compute without document context (`lufs` momentary, `peak`, `rms`).
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---
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## 4. File layout
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```text
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packages/media/audio/audio-analysis-loudness/
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package.json, tsconfig.json, vitest.config.ts, README.md
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src/
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index.ts
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error-codes.ts
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meter/
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loudness-meter.ts (+ .md .types.ts .schemas.ts .test.ts) · index.ts
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algorithms/
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lufs.ts (+ .md .test.ts)
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true-peak.ts (+ .md .test.ts)
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loudness-range.ts (+ .md .test.ts)
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index.ts
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filters/
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k-weighting.ts (+ .md .test.ts)
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index.ts
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__benchmarks__/
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loudness.bench.ts
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tests/
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integration.test.ts property.test.ts purity.test.ts exports.test.ts
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```
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`algorithms/` holds the pure DSP kernels (no `AudioDocument` knowledge — they take `Float32Array[]`
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and numbers); `filters/` holds the K-weighting cascade; `meter/` is the `AnalysisOp` orchestration
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layer that wires document streaming, the gating engine, OTel, Zod validation, and abort handling
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together. Each `algorithms/*` and `filters/*` module is independently subpath-exported so a
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consumer that only needs true-peak detection does not pull the gating engine.
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---
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## 5. Integration notes
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- **`@suaveplan/audio-core`** — supplies `AudioDocument`, the `AnalysisOp` / `AnalysisResult`
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interfaces, `BlockContext`, and the read/stream APIs the meter consumes. The meter reads PCM
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through `doc.stream()` so it inherits core's paged-memory and AbortSignal behaviour for free.
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- **`@suaveplan/error`** — `AudioError` base class and the `AUDIO_ANALYSIS` code namespace
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(`AUDIO_ANALYSIS_LOUDNESS.INVALID_OPTIONS`, `AUDIO_ANALYSIS_LOUDNESS.EMPTY_DOCUMENT`, `AUDIO_ANALYSIS_LOUDNESS.ABORTED`).
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- **`@suaveplan/opentelemetry`** — span `audio.analysis.loudness`, counter
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`audio_analysis_runs_total`, histograms `audio_analysis_duration_ms` and
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`audio_analysis_block_duration_ms`, all tagged `{op="loudness-meter"}`. Instrumentation is
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lazy — inert with no exporter, never an import-time side effect.
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- **`@suaveplan/types`** — `LoggerLike` for the optional injected logger.
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- **`zod`** — `LoudnessMeterOptionsSchema` validates the constructor and entry-point options;
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failures throw `AUDIO_ANALYSIS_LOUDNESS.INVALID_OPTIONS` with the Zod issue list in `context`.
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---
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## 6. Benchmarks
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- `loudness.bench.ts` — `analyze` a 1-minute 48 kHz stereo track.
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- `loudness.bench.ts` — `analyze` a 10-minute 48 kHz stereo track (verifies the gating engine
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stays linear and the streaming path does not accumulate per-block allocation).
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---
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## 7. Decisions and trade-offs
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- **One gating engine, two entry points.** Rather than a separate fast-path approximation for
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streaming, `analyzeStream` yields the *same* engine's running state. This guarantees the streamed
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result converges exactly to the batch result and removes a whole class of "streaming disagrees
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with batch" bugs at the cost of `analyzeStream` doing no less work than `analyze`.
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- **Silence floors instead of `-Infinity`.** BS.1770 loudness of true silence is `-Infinity`;
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returning that value forces every consumer (normalizers, React meters) to special-case it. The
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meter clamps `lufs` and `rms` to finite BS.1770 floor values so the result shape is always
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numeric. This is a deliberate, documented deviation from a naive reading of the standard.
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- **`algorithms/` kernels are document-agnostic.** The LUFS, true-peak, and loudness-range kernels
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take `Float32Array[]` and plain numbers, not `AudioDocument`. This keeps them unit-testable
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against synthetic signals with no core dependency in the test, and lets the FX package reuse the
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true-peak kernel directly for a true-peak limiter without instantiating a meter.
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- **True-peak via fixed 4x oversampling.** BS.1770-4 permits higher oversampling ratios, but 4x is
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the specified minimum and is sufficient up to 48 kHz material; a configurable ratio would add
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surface area for negligible accuracy gain in the target sample-rate range. If a future consumer
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needs 8x for very-high-rate material it can be added as an option without breaking the result
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shape.
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- **No browser `AnalyserNode` path.** Unlike `audio-analysis-spectrum`, loudness metering needs
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exact gated energy, not a smoothed FFT — there is no correctness-preserving `AnalyserNode`
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shortcut, so the package stays purely universal with a single hand-rolled DSP path.
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