Over-the-Ear Headphone Frequency Response Target

• The paper presents an IDE-based method that uses real-time listener feedback and paired comparisons to optimize over-the-ear headphone frequency response targets.
• It employs a parametric representation of 10 octave-band gains constrained between -3 and +3 dB, facilitating efficient search and perceptual adjustments.
• Experimental results demonstrate systematic convergence with improved listener ratings and statistically significant preferences for the best-evolved curves.

An over-the-ear headphone frequency response target is a reference equalization curve representing the collective frequency response preferences of listeners for over-the-ear (circumaural) headphones. Recent methodologies integrate real-time listener feedback with adaptive algorithms to empirically derive target curves, optimizing design and tuning processes for consumer satisfaction. One notable approach employs an Interactive Differential Evolution (IDE) framework to iteratively evolve and converge populations of parametric frequency-response curves via adaptive paired rating experiments, enabling target discovery even among untrained listeners (Ravizza et al., 9 Dec 2025).

1. Parametric Representation of Headphone Frequency Response Targets

In the IDE-based paradigm, each candidate frequency response is represented as a vector of $D=10$ octave-band gains in decibels, covering the range from 31 Hz to 16 kHz. Let $r \in \mathbb{R}^D$ denote an individual target curve, where each element $r_i \in [-3\,\text{dB},+3\,\text{dB}]$ corresponds to the gain at the $i$th band ($f_1=31$ Hz, $f_{10}=16$ kHz). This parameterization facilitates efficient search and human interpretability, with all curve variants constrained within bounds chosen to both ensure plausibility and prevent excessive coloration.

The initial reference curve—typically a median derived from previous preference studies—serves as the evolutionary seed. This approach enables direct adaptation to a listener panel’s specific collective response without preconceived assumptions about optimal curve shape.

2. Adaptive Interactive Differential Evolution Method

The adapted IDE algorithm operationalizes the discovery of preferred target curves via a human-in-the-loop, population-based optimization process:

1. Initialization: For each listener, a population of $NP=5$ individuals is generated by perturbing each band of the median reference within $[-3,+3]$ dB.
2. Iteration: Over $G=8$ generations, each individual undergoes mutation and crossover; newly generated candidates are subject to bounds-clipping.
3. Selection via Listening Tests: Listeners evaluate pairs (current vs. candidate) using a continuous bipolar scale ($s_i \in [-1,+1]$). The sign of $s_i$ determines selection—if $s_i>0$, the candidate survives; else, the original is retained.
4. Parameter Choices: $F=0.2$ (mutation scaling) and $C=0.7$ (crossover rate), selected to balance exploration and rapid information sharing.
5. Stimulus Presentation: 15–30 s music excerpts, randomly drawn from 8 tracks, are filtered in real time via corresponding individual curves, with overall playback loudness equalized to $-18$ LUFS and hardware compensation (DT770 Pro 250 Ω) applied.
6. Total Workload: $NP \times G = 40$ paired comparisons per listener, designed to limit fatigue while sufficiently exploring the high-dimensional space.

This process efficiently narrows the solution space based on direct, iterative human auditory preference, supporting robust target extraction even from panels of listeners lacking formal auditory training (Ravizza et al., 9 Dec 2025).

3. Experimental Protocol and Evaluation Metrics

The methodology was empirically validated in a study with 24 Japanese adult students (main IDE experiment, all self-reported normal hearing, untrained in critical listening), supplemented by a follow-up benchmark with 22 additional participants.

• Main Experiment: Each listener completed 40 pairwise comparisons under the IDE protocol.
• Benchmarking: The final evolved population (5 individuals) plus a flat-response anchor were tested in a standard multiple-stimulus evaluation (6 curves × 8 tracks = 48 trials per listener).

Convergence Metrics included:

• Population Standard Deviation per Band ($\langle SD \rangle_g$): Aggregated across listeners and bands for each generation, quantifying global population spread at every stage.
• Preference Odds Ratio: Via logistic GLMM, comparing the final (“best”) evolved curve to the initial reference.

4. Results: Convergence and Consensus Analysis

The population’s spread, quantified by $\langle SD \rangle_g$ [dB], decreased monotonically over generations: 1.72 (g=1), 1.51, 1.38, 1.28, 1.19, 1.12, 1.04, and 0.98 (g=8). This reflects systematic convergence in listener preferences within the parameter search space.

In the multiple-stimulus test, the best-evolved curve achieved a mean listener rating of 3.74 (95% CI ±0.09) on a 1–5 scale, compared to 3.51 (±0.08) for the initial reference. The odds ratio favoring the best curve was 1.29 ($z=2.72$, $p=0.018$), indicating statistically significant preference among participants.

Individual preference curves at generation 8 displayed within-band SD $\approx1$ dB; dispersion did not correlate strongly with age, gender, or self-reported listening experience, suggesting a relatively homogeneous consensus within the experiment’s cohort. The study did not publish exact band-specific target values but confirmed parameter bounds ($\pm3$ dB) and convergence to approximately 1 dB SD as indicative of group consensus at practical JND limits (Ravizza et al., 9 Dec 2025).

5. Practical Guidelines and Methodological Limitations

Recommended implementation strategies based on empirical findings:

• Population Size: NP in [3,7] optimizes fatigue vs. search coverage.
• Algorithm Parameters: Default $F\approx0.2-0.3$, $C\approx0.6-0.8$; suit tuning to stimulus and application.
• Session Duration: Capped at ~30 min (40–50 comparisons).
• Playback Calibration: Strict system pre-compensation to ensure flat reference response.
• Monitoring Convergence: Halt IDE if $\langle SD \rangle_g$ falls below perceptual discrimination JND ($\approx0.5$ dB).
• Logging: Record continuous listener ratings for diagnostic analysis, even if only binary outcomes inform selection.

Strengths of this approach include real-time human-in-the-loop optimization without preselected responses, scalability to novice listeners, and completion within a single session. Limitations include final target resolution not reaching sub–1 dB, parameter sensitivity (requiring further pilot tuning), and increased complexity relative to fixed A/B testing paradigms.

6. Extension, Future Directions, and Impact

Potential refinements for the IDE methodology and frequency response target discovery include:

• Dynamic Parameter Adaptation: Modify $F$ and $C$ in real time to accelerate convergence as the solution space collapses.
• Per-Band JND Models: Employ explicit JNDs for adaptive stopping criteria and precision targeting.
• Generalization: Application to in-ear and open-back headphones, beyond circumaural design.
• Mass-Customization: Scaling methodology for large-scale consumer crowdsourcing of personalized headphone equalization preferences.

The IDE-based target discovery method supports rapid, empirical extraction of consumer-preferred response curves in audio personalization contexts, providing detailed algorithmic and empirical guidance for further research and commercial implementation (Ravizza et al., 9 Dec 2025).