Reference-Based Recursive Least-Squares Mitigation of Real Interference in Stereo Audio Recordings

Necati Kagan Erkek; Y. Ugur Ozcan

arxiv: 2606.18564 · v1 · pith:DHXIQNRDnew · submitted 2026-06-17 · 💻 cs.SD · eess.SP

Reference-Based Recursive Least-Squares Mitigation of Real Interference in Stereo Audio Recordings

Necati Kagan Erkek , Y. Ugur Ozcan This is my paper

Pith reviewed 2026-06-26 20:14 UTC · model grok-4.3

classification 💻 cs.SD eess.SP

keywords adaptive interference cancellationrecursive least-squaresstereo audio recordingstrain noisereference-based filteringreal environmental interferenceno-reference performance metrics

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The pith

Real train interference in stereo audio can be substantially attenuated using a correlated reference recording and multi-reference recursive least-squares estimation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper evaluates whether a second stereo recording of train noise can serve as a reference to cancel interference in primary stereo audio captures. It models the observed signal as clean program plus additive disturbance from unknown paths, then uses the reference in an RLS estimator to subtract the estimated interference before low-pass filtering. With no ground truth available, it measures success by drops in waveform correlation to the reference and changes in RMS level. The approach matters because many real-world recordings suffer from environmental noise where a second microphone placement could provide the needed reference. If the method works, it shows adaptive filtering can handle real acoustic effects beyond lab simulations.

Core claim

With 30 taps per reference channel, 15 anti-causal taps, and forgetting factor 0.999, processing three 74-second real sequences reduces the maximum reference correlation from 0.386-0.832 to 0.011-0.016, achieving a correlation-ratio reduction of 30.6-34.1 dB and RMS decreases of 1.8-4.8 dB, demonstrating that real train interference including environmental acoustic effects can be substantially attenuated when a correlated reference recording is available.

What carries the argument

Multi-reference recursive least-squares (RLS) estimator that uses the second stereo recording to model and subtract the unknown propagation paths of the train noise.

If this is right

The estimated interference component is subtracted from the noisy stereo audio.
A finite-impulse-response low-pass postfilter is applied after subtraction.
Reference correlation drops to 0.011-0.016 after processing.
Output RMS level decreases by 1.8-4.8 dB depending on section and channel.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This technique could extend to canceling other correlated environmental noises in field recordings if a suitable reference channel exists.
Real-time implementations might benefit from the forgetting factor of 0.999 for tracking slowly varying noise.
Testing on additional noise types would reveal how much the correlation between reference and primary must exceed a threshold for effective cancellation.

Load-bearing premise

The second stereo recording must be a sufficiently correlated filtered observation of the identical physical noise source that reaches the primary microphones.

What would settle it

If processing leaves residual normalized correlation with the reference above 0.05 or fails to reduce it by at least 20 dB, the claim of substantial attenuation would not hold.

Figures

Figures reproduced from arXiv: 2606.18564 by Necati Kagan Erkek, Y. Ugur Ozcan.

**Figure 2.** Figure 2: Noisy input and reference signals for Sections A–C, shown for the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** Figure 4: Time-domain comparison between the noisy input and the final estimate [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Welch PSD estimates for the left channel. The RLS stage reduces [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: Reduction of the maximum residual normalized correlation with the [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

read the original abstract

Reference-based adaptive interference cancellation is evaluated for stereo audio recordings corrupted by real train noise and environmental background. The observed signal is modeled as a clean stereo program contaminated by an additive disturbance generated by an external acoustic source through unknown propagation paths. A second stereo recording, representing another filtered observation of the same physical noise source, is used as the reference input of a multi-reference recursive least-squares (RLS) estimator. The estimated train-interference component is subtracted from the noisy audio and followed by a finite-impulse-response low-pass postfilter. Three 74.01 s real audio sequences sampled at 11.025 kHz are processed under identical algorithmic parameters. Since clean ground truth is not available, performance is assessed with no-reference indicators: waveform behavior, Welch spectral estimates, RMS change, and residual normalized correlation with the reference. With 30 taps per reference channel, 15 anti-causal taps, and forgetting factor 0.999, the maximum reference correlation is reduced from 0.386--0.832 before processing to 0.011--0.016 after processing. The corresponding correlation-ratio reduction is approximately 30.6--34.1 dB, while the output RMS decreases by 1.8--4.8 dB depending on section and stereo channel. The results demonstrate that real train interference, including environmental acoustic effects, can be substantially attenuated when a correlated reference recording is available.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Standard multi-reference RLS cuts reference correlation by ~30 dB on three real train-noise recordings, but the 45-tap FIR support is too short to model full acoustic paths and the method itself is not new.

read the letter

The paper takes a known multi-reference RLS algorithm and runs it on three 74-second real stereo recordings of train noise at 11 kHz, using a second stereo pair as the reference. With 30 taps per reference channel, 15 anti-causal taps, and forgetting factor 0.999, it reports the normalized correlation with the reference falling from 0.386-0.832 down to 0.011-0.016, plus modest RMS drops. They subtract the estimated interference and apply a simple FIR low-pass afterward.

What it does well is stay honest about the lack of clean ground truth and stick to no-reference checks: waveform plots, Welch spectra, RMS change, and the correlation metric. The numbers are consistent with what the estimator should produce on correlated inputs, and the real recordings include whatever environmental filtering actually occurred.

The main limitation is the filter length. At 11 kHz the total support is only about 4 ms. Acoustic paths from a distant moving train routinely have reverberation tails longer than that, so the RLS can only cancel the short-time correlated component. The observed correlation drop is therefore real but probably partial. Three short sequences also give no sense of variability across different conditions or microphone placements. The algorithm and the evaluation approach are standard in the adaptive-filtering literature; the contribution is the specific empirical case.

This is useful for engineers who already do reference-based cancellation and want to see how the method behaves on actual field recordings of train noise rather than simulations. Readers looking for new theory or broader applicability will not find it. The work is transparent enough to deserve a serious referee, mainly for the real-data results, though reviewers will likely press on the tap-length issue and ask for more recordings or statistical checks. I would send it to review.

Referee Report

1 major / 0 minor

Summary. The paper claims that a multi-reference recursive least-squares (RLS) adaptive filter, using a second stereo recording as reference input, can substantially attenuate real train noise (including environmental acoustic effects) in primary stereo audio recordings. The observed signal is modeled as clean program plus additive disturbance through unknown paths; the RLS estimator (30 taps per reference channel + 15 anti-causal taps, forgetting factor 0.999) subtracts the estimated interference, followed by an FIR low-pass postfilter. On three 74.01 s real recordings sampled at 11.025 kHz, no-reference metrics show reference correlation reduced from 0.386–0.832 to 0.011–0.016 (≈30.6–34.1 dB) and RMS reduced by 1.8–4.8 dB.

Significance. If the central empirical claim holds, the work demonstrates practical viability of reference-based RLS cancellation for real acoustic interference where ground-truth clean signals are unavailable. Credit is due for processing actual field recordings rather than simulations and for consistent use of no-reference metrics (correlation, RMS, Welch spectra) that directly measure residual disturbance.

major comments (1)

[Abstract and method description] Abstract and method description: the claim that the approach models 'unknown propagation paths' including 'environmental acoustic effects' is undercut by the chosen FIR support. With 30 taps per channel + 15 anti-causal taps at 11.025 kHz the total support is only ~4 ms; real reverberant paths from a distant train routinely exceed this length. The reported 30 dB correlation drop is therefore consistent with cancellation of only the short-time correlated component, weakening the assertion of comprehensive attenuation of the full disturbance.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment regarding filter support and its relation to the modeling of propagation paths. We respond to the major comment below.

read point-by-point responses

Referee: [Abstract and method description] Abstract and method description: the claim that the approach models 'unknown propagation paths' including 'environmental acoustic effects' is undercut by the chosen FIR support. With 30 taps per channel + 15 anti-causal taps at 11.025 kHz the total support is only ~4 ms; real reverberant paths from a distant train routinely exceed this length. The reported 30 dB correlation drop is therefore consistent with cancellation of only the short-time correlated component, weakening the assertion of comprehensive attenuation of the full disturbance.

Authors: The referee correctly notes that 45 taps at 11.025 kHz span only ~4 ms. The multi-reference RLS estimator adapts to the effective linear mapping between reference and primary channels over this finite support, which includes the direct path and early reflections responsible for the observed short-time correlation. The 30.6–34.1 dB reduction in normalized correlation demonstrates that these correlated components—incorporating environmental acoustic effects within the modeled length—are substantially attenuated. We do not claim to cancel infinite-length reverberation tails beyond the filter support. To avoid any overstatement, we will revise the abstract and method sections to clarify that the method targets the short-time correlated portion of the disturbance. revision: yes

Circularity Check

0 steps flagged

No circularity: direct empirical measurements on real recordings

full rationale

The paper applies a standard multi-reference RLS algorithm (with fixed parameters: 30 taps, 15 anti-causal taps, forgetting factor 0.999) to three real 74 s stereo recordings at 11.025 kHz and reports measured no-reference metrics (residual correlation, RMS change, spectral estimates) on the processed outputs. The central claim follows directly from these waveform-level observations rather than from any fitted parameter being renamed as a prediction or from a self-citation chain. No derivation step reduces to its own inputs by construction; the work is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that a second stereo recording provides a usable reference observation of the identical noise source. No new entities are postulated. The number of taps and forgetting factor are chosen parameters rather than fitted constants.

free parameters (3)

number of taps per reference channel
Set to 30; chosen to balance modeling capacity and computational cost for the 11.025 kHz sampling rate.
number of anti-causal taps
Set to 15; chosen to allow non-causal filtering of the reference.
forgetting factor
Set to 0.999; chosen to give slow adaptation suitable for stationary train noise.

axioms (1)

domain assumption The observed signal is a linear combination of the clean program and an additive disturbance that can be modeled as a filtered version of the reference recording.
Stated in the abstract as the signal model underlying the RLS estimator.

pith-pipeline@v0.9.1-grok · 5790 in / 1424 out tokens · 20259 ms · 2026-06-26T20:14:41.345083+00:00 · methodology

discussion (0)

Reference graph

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