hearing-aid-compensation.md

Hearing Aid Compensation: Algorithms, Terms, and Implementation

This document is written for readers who have basic signal-processing background but have not worked deeply on hearing-aid DSP.

It has three goals:

1. Explain why HearAdjust currently caps manual gain at +40 dB, and why that is an implementation constraint rather than a medical threshold.
2. Explain the common hearing-aid algorithms and technical terms in a coherent DSP framework.
3. Explain how those algorithms are typically implemented, and how that differs from the current project.

1. Separate the concepts that are easiest to confuse

1.1 dB HL is not the same thing as dB gain

• dB HL is an audiometric hearing-threshold scale.
• dB gain is signal gain applied inside an audio processing chain.

They are not related by a direct one-to-one mapping.

Reasons include:

• target compensation depends on frequency
• target compensation depends on input level
• a hearing aid must balance audibility, comfort, and maximum output

So a 40 dB HL loss at one frequency does not imply that +40 dB fixed playback gain is the correct engineering choice.

1.2 EQ is not the whole hearing aid, only one module

EQ, short for equalization, is a system that imposes a frequency response $H(e^{j\omega})$ so that different spectral components experience different gains.

In simple terms:

• low frequencies may be amplified
• mids may remain flat
• highs may be attenuated

That is EQ.

But real hearing-aid DSP typically includes more than static equalization:

• dynamic compression
• output limiting
• feedback cancellation
• noise reduction
• directionality
• frequency lowering

So EQ should be thought of as one foundational block in a hearing-aid chain, not as the complete device logic.

1.3 Static compensation versus dynamic compensation

Static compensation:

• a given band receives the same gain regardless of input level

Dynamic compensation:

• soft input receives more gain
• loud input receives less gain

Modern hearing-aid processing is usually built around the latter.

2. What HearAdjust currently implements

The current Hearing Aid Mode in this project is fundamentally an 8-band cascaded peaking EQ.

Current characteristics:

• each band is a BiquadFilterNode
• filter type is peaking
• center frequencies are fixed at 250, 500, 750, 1000, 2000, 4000, 6000, and 8000 Hz
• Q = 1.5 is fixed
• only the band gain changes
• the overall graph is approximately source -> 8-band EQ -> destination

So the current system is:

• a parametric equalizer
• with fixed center frequencies and fixed Q
• with variable per-band gain
• whose overall response is approximately the product of the cascaded band responses

It does not currently include:

• per-band envelope detection
• wide dynamic range compression
• a dedicated output limiter
• adaptive feedback cancellation
• high-frequency lowering

For that reason, the current implementation is closer to a personal compensation EQ than to a full hearing-aid processing chain.

3. What a peaking EQ actually is

Peaking EQ, also called a peaking filter or bell EQ, has a bell-shaped magnitude response.

• with positive gain, it creates a peak around a center frequency
• with negative gain, it creates a dip around that center frequency

Its main parameters are:

3.1 Center frequency f0

Determines where the peak or dip is centered.

3.2 Gain

Determines whether that band is boosted or cut.

• +6 dB increases magnitude around the band
• -6 dB decreases magnitude around the band

3.3 Quality factor Q

Determines how wide the affected band is.

• larger Q means narrower bandwidth
• smaller Q means wider bandwidth

For the current project:

• Q = 1.5 is moderately broad
• each control point affects a neighborhood of frequencies rather than an infinitesimal single tone

4. Why the current +40 dB ceiling is an implementation ceiling, not a theoretical one

The current implementation is static EQ without dedicated output protection. Under that design, high positive gain quickly causes practical problems.

4.1 Multiple boosts reduce headroom

If several bands are boosted simultaneously, time-domain peaks can increase significantly.

Even when each band looks acceptable in isolation, the recombined output can still create:

• clipping
• inter-sample peak risk
• harsh distortion

4.2 Noise and artifacts are amplified as well

Compensation gain boosts not only useful speech content but also:

• background noise
• codec artifacts
• reverberant tails
• sibilance and hiss

4.3 Static EQ does not handle loudness recruitment

Sensorineural hearing loss often behaves less like a rigid shift and more like:

• soft sounds are inaudible
• loud sounds quickly become uncomfortable

That is one reason why real hearing aids rely on WDRC rather than just large fixed gains.

4.4 Without limiting, both stability and comfort are weaker

If the UI ceiling is pushed to +50 dB or +60 dB without limiter or MPO control, the system becomes easier to overload and harder to use comfortably.

5. Common hearing-aid algorithms and terms, explained as a signal chain

It is easiest to understand them in the order they appear in a more typical processing chain.

input
  -> preprocessing / conditioning / calibration
  -> crossover or filter bank
  -> per-band envelope detection
  -> per-band WDRC
  -> optional noise reduction / speech enhancement / directionality control
  -> optional frequency lowering
  -> recombination
  -> output limiter / MPO
  -> receiver

5.1 Prescriptive fitting formulas

Common examples include:

• NAL-NL2
• DSL v5

These are not the audio processors themselves. They are target-generation methods.

Their inputs often include:

• the audiogram
• user category or age
• binaural context
• audibility and intelligibility goals

Their outputs are typically:

• target gain by frequency and input level

So they serve more as parameter generators for dynamic hearing-aid processing than as direct filter implementations.

5.2 Filter bank or crossover

This is the front end of a multichannel hearing aid.

Purpose:

• split broadband input into subbands
• allow each subband to be processed independently

Common implementation choices:

• IIR crossovers
• FIR analysis filter banks
• FFT or STFT subband processing
• gammatone or auditory-inspired filter banks

Tradeoffs:

• IIR: cheap and low-latency, but phase and crossover interaction require care
• FIR: easier phase control, but higher order and latency
• STFT: convenient for noise reduction and speech enhancement, but block latency and windowing become important

5.3 Envelope detector

WDRC usually does not react to the raw waveform directly. It first estimates subband level or envelope.

Common methods:

• full-wave rectification followed by low-pass filtering
• RMS detector
• Hilbert envelope
• peak detector

Key design questions:

• time constants
• peak sensing versus RMS sensing
• attack and release smoothing

Peak detectors:

• respond more strongly to transients
• are often useful for protection

RMS detectors:

• track average energy more closely
• usually yield smoother subjective behavior

5.4 WDRC, Wide Dynamic Range Compression

This is one of the central dynamic processing blocks in hearing aids.

Goal:

• make soft sounds audible
• keep medium sounds natural
• keep loud sounds tolerable

From an input-output curve perspective:

• below a kneepoint, gain is relatively high
• above it, output grows more slowly than input

Common parameters:

• TK, compression threshold or kneepoint
• CR, compression ratio
• attack
• release
• make-up gain or insertion gain

In a piecewise-linear view, a common interpretation is:

• when input level L_in is below TK, apply a higher effective gain
• when L_in exceeds TK, reduce gain according to the compression ratio

The compressed segment slope is often written as:

1 - 1/CR

When CR > 1, each additional 1 dB at the input produces less than 1 dB increase at the output.

5.5 AGC, Automatic Gain Control

In the broad literature, AGC can refer to many kinds of dynamic gain adjustment.

In hearing-aid discussions it is useful to distinguish:

• slow AGC for overall loudness adaptation
• faster WDRC for audibility and comfort shaping
• output AGC or limiting for overload protection

So AGC is better viewed as a broad family, with WDRC as one important subtype.

5.6 MPO, Maximum Power Output

MPO is about keeping the output from becoming too intense.

It is generally implemented near the end of the chain.

Purpose:

• limit strong peaks
• prevent output overload
• preserve subjective comfort

It is primarily a protection and comfort mechanism, not a speech-enhancement algorithm.

5.7 Limiter versus compressor

Both are dynamic range processors.

The practical difference is in degree and purpose:

• a compressor changes dynamic range more gradually
• a limiter uses high ratio and fast response to stop peaks

A common architecture is:

• per-band WDRC first
• then a fast broadband limiter at the output

5.8 Noise reduction

Hearing-aid noise reduction is usually not trying to remove noise completely. It aims to:

• improve comfort
• reduce sustained background load
• preserve speech while suppressing less useful energy

Common methods include:

• spectral subtraction
• Wiener filtering
• MMSE-style estimators
• modulation-domain filtering
• DNN-based speech enhancement

Engineering constraints are usually:

• low latency
• stable behavior
• minimal musical noise

That is why commercial systems are often conservative.

5.9 Directionality and beamforming

With multiple microphones, a device can exploit spatial information to improve SNR.

Common approaches:

• fixed beamformers
• adaptive beamformers
• binaural beamforming

This matters because improving input SNR often helps more than adding another +6 dB of gain later.

But a browser extension that captures tab audio does not generally have access to a real microphone array or acoustic scene, so this part does not map directly to the current project.

5.10 Feedback cancellation

At high gain, an important problem is acoustic feedback:

• the receiver emits sound
• the microphone picks it back up
• a loop is formed
• whistling appears

Common solutions:

• adaptive estimation of the feedback path
• LMS, NLMS, or related adaptive filters
• subtraction of the estimated feedback component from the microphone signal

Engineering difficulty:

• the real feedback path changes with fit and positioning
• correlation between feedback and desired input can cause misadjustment

5.11 Frequency lowering

When high-frequency hearing loss is severe, more treble gain may no longer be useful and may instead increase:

• noise
• feedback risk
• harshness

That is when frequency lowering becomes attractive.

Common families:

• frequency compression
• frequency transposition
• frequency translation

Typical steps:

• detect high-frequency content or features
• shift or compress it into a lower target region
• blend it with the original or adjacent bands

Main difficulties:

• metallic artifacts
• altered speech spectral cues
• high parameter sensitivity

6. How a typical multiband WDRC implementation is built

Here is the same idea from a more engineering-oriented view.

6.1 Band splitting

Split input into subbands:

x[n] -> x1[n], x2[n], ..., xM[n]

6.2 Per-band level estimation

For example:

• rectification followed by low-pass filtering
• or short-window RMS

This yields a level estimate L_i[n] for each band.

6.3 Map level to target gain

For band i, define a level-to-gain mapping:

G_target_i = f_i(L_i)

The function f_i usually comes from:

• the audiogram
• the fitting rule
• fitted target points across different input levels

6.4 Smooth the gain with attack and release

Direct instantaneous gain jumps would create:

• pumping
• zipper noise
• modulation distortion

So a first-order smoother or separate attack and release constants are typically used.

6.5 Apply gain and reconstruct

y_i[n] = g_i[n] * x_i[n]
y[n] = sum_i y_i[n]

6.6 Add output protection

Common final stages are:

• broadband limiter
• output AGC
• MPO control

7. Common implementation choices and tradeoffs

7.1 IIR versus FIR

IIR advantages:

• low computation
• low latency
• good fit for real-time devices

IIR disadvantages:

• nonlinear phase
• crossover interaction must be designed carefully

FIR advantages:

• linear phase is possible
• magnitude shaping is intuitive

FIR disadvantages:

• longer filters can mean larger latency
• hearing-aid pipelines are very latency-sensitive

7.2 Time-domain filter banks versus STFT

Time-domain filter banks:

• easier latency control
• historically common in low-latency hearing-aid systems

STFT:

• more flexible frequency-domain processing
• convenient for denoising and speech enhancement
• but block processing usually increases delay

7.3 Low-latency constraints

Hearing-aid systems are extremely sensitive to delay.

Excess delay can create:

• echo-like sensation
• unnatural self-voice perception
• poor wear comfort

That is why long windows, deep buffers, and heavy iterative processing are often avoided in real-time assistive pipelines.

8. How HearAdjust differs from a typical hearing aid today

The current Hearing Aid Mode does provide:

• fixed-frequency EQ control
• manual per-band gain
• basic audibility compensation

But it is missing several core hearing-aid capabilities.

8.1 No level-dependent gain

Band gain does not depend on the input level.

That means:

• soft and loud sounds are amplified similarly
• loudness recruitment is not handled well

8.2 No dedicated output protection

There is no independent MPO or final limiter.

So under high gain the most immediate engineering risks are:

• clipping
• reduced comfort

8.3 No ear-specific, scene-specific, or level-specific fitting

Real hearing aids often vary by:

• left versus right ear
• quiet versus speech versus noise environments
• soft versus medium versus loud inputs

The current project does not yet include those axes of adaptation.

9. A sensible evolution path for this repository

Stage 1. Add output protection after the current EQ

Recommended additions:

• pre-gain headroom control
• post-EQ limiter or compressor
• peak monitoring

Meaning:

• first solve the engineering problem of overload under high gain

Stage 2. Introduce multiband WDRC

Recommended additions:

• stop treating gain as fixed per band
• add envelope detection and dynamic gain per band
• derive target curves from audiograms and fitting rules

Meaning:

• move from graphic compensation EQ toward a dynamic hearing compensation processor

Stage 3. Add advanced modules

For example:

• frequency lowering
• adaptive noise reduction
• separate left/right fitting
• context-aware presets

10. Most important conclusions for the current project

Conclusion 1

The current +40 dB ceiling is primarily an implementation safety limit, not a medical boundary.

Conclusion 2

Without limiter, MPO control, and WDRC, simply extending the slider range tends to make the system noisier, more distortion-prone, and less stable.

Conclusion 3

If stronger compensation is needed, the next step should not be “more static EQ”. It should be “level-dependent multiband processing”.

11. Quick glossary

• EQ: a system that changes gain as a function of frequency
• peaking EQ: a bell-shaped boost or cut around a center frequency
• Q: quality factor controlling bandwidth
• filter bank: a set of filters that splits the signal into subbands
• WDRC: wide dynamic range compression; more gain for soft sounds, less for loud sounds
• AGC: automatic gain control; a broad family of level-dependent gain control
• MPO: maximum power output control
• limiter: a high-ratio, fast-acting peak restrainer
• beamforming: spatial filtering using multiple microphones
• feedback cancellation: estimation and subtraction of the feedback path
• frequency lowering: moving high-frequency information into a lower audible region

12. Sources consulted

• MDN Web Docs: DynamicsCompressorNode
• Wikipedia: Hearing aid
• Wikipedia: Dynamic range compression

These notes are intended as technical guidance for engineering understanding and implementation, not as medical fitting advice.