Continued fractions and passive ladder networks for acoustic impedances: the baffled piston and the horn

Ronald M. Aarts

Home/Archive/arXiv

arXiv · 2610.20371

Continued fractions and passive ladder networks for acoustic impedances: the baffled piston and the horn

Ronald M. Aarts

View original source ↗Read source document ↗Export metadata ↓

Abstract

Lumped-element networks give transparent, passive models of acoustic impedances whose low- and high-frequency limits can be read from the circuit, but a systematic, arbitrarily accurate construction for non-rational impedances is lacking. Continued fractions, one- and two-point Padé approximants and their identity with ladder networks and Cauer synthesis are introduced in tutorial form and applied to two examples: the radiation impedance of a baffled circular piston and the throat impedance of a horn with a piston mouth. The even contraction of the piston's continued fraction has positive coefficients, certified by interval arithmetic for the first 100 pairs, and yields a ladder of positive resistances, masses and compliances; with 14 elements the error is 4e-4 up to ka = 5. Beranek's four-element network is, to about 2%, the order-two two-point Padé approximant. A horn modelled as a cascade of waveguide sections is a continued fraction whose tail is the mouth impedance; the infinite exponential horn is a periodic continued fraction, an exact high-pass ladder. The piston networks are passive at every certified order (up to 202 elements) and are extended without changing existing elements; for a finite horn the error of the mouth network passes one to one to the throat impedance.

Explore related subjects

eess.AS physics.class-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Ronald M. Aarts. 2026-10-14. Continued fractions and passive ladder networks for acoustic impedances: the baffled piston and the horn. https://arxiv.org/abs/2610.20371

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

VoxTurn: Answering Several Turn-Taking Questions in One Pass with One Model

A cascaded voice agent must decide, throughout each silence of its user, whether the user has finished their turn: answering too early cuts the user off, answering too late makes the agent slow. It often needs related decisions too: will the user soon go on, is speech during its own turn an interruption or a backchannel, is a sound speech at all. With open detectors, each extra decision costs another model or another call, and on the 14-language eot-bench they cut users off in more than a quarter of mid-turn pauses. Because they are trained on segmented utterances, this mismatch is the largest single source of error. We present VoxTurn, a 0.8B speech LLM that casts these decisions as multiple-choice questions, scores the hidden state of each option, and answers any set of them in one forward pass with a block-isolating attention mask, exactly as if asked one at a time. Trained on real conversational pauses with labels derived from their timing, and re-queried while a silence lasts, VoxTurn reaches 11.5% false cut-offs in English at a 300 ms latency budget, comparable to two commercial detectors, and a 14-language mean of 19.9%, the lowest among open models, at 8.3 ms per decision. In Pipecat and LiveKit it cuts off 17% and 9% of turns, and it ranks fifth of 24 in TurnBench end-of-turn detection without any TurnBench training data. The model, code and framework plugins are released.

eess.AS↗

arXiv2026

Full-Duplex Interaction with Speech, Expressions and Gestures

Human face-to-face conversation requires coordinating speech, gestures and expressions across both speaking and listening. We present ELLSA 2, an end-to-end full-duplex dialogue model that jointly optimizes speech interaction and streaming gesture-expression generation. An autoregressive, chunk-wise synthesizer combines pretrained acoustic features with distinct listening and speaking hidden states from the dialogue backbone and speech synthesizer, enabling continuous non-verbal generation even when the model is verbally silent. To translate dialogue understanding into vivid semantic gestures, we introduce contextual semantic calls and template guidance, separating whether to invoke an available semantic gesture from how to realize it. We also establish a curated data and evaluation pipeline for dialog-aware co-speech gesture generation and investigate reference-based multimodal large language models (MLLMs) as automatic judges. Experiments show that ELLSA 2 remains highly competitive with open-source full-duplex speech interaction models and outperforms cascaded baselines across dialog-aware gesture and expression metrics. Semantic template guidance further significantly improves semantic gesture quality. Strong system-level correlations with human judgments support these reference-based scores as useful preliminary metrics for full-duplex and semantic gesture assessment. Together, these results advance dialogue modeling from spoken responses toward coordinated multimodal interaction.

eess.AS↗

arXiv2026

Conditional Flow Matching for Visually-Guided Acoustic Highlighting

Visually-guided acoustic highlighting seeks to rebalance audio in alignment with the accompanying video, creating a coherent audio-visual experience. While visual saliency and enhancement have been widely studied, acoustic highlighting remains underexplored, often leading to misalignment between visual and auditory focus. Existing approaches use discriminative models, which struggle with the inherent ambiguity in audio remixing, where no natural one-to-one mapping exists between poorly-balanced and well-balanced audio mixes. To address this limitation, we reframe this task as a generative problem and introduce a Conditional Flow Matching (CFM) framework. A key challenge in iterative flow-based generation is that early prediction errors -- in selecting the correct source to enhance -- compound over steps and push trajectories off-manifold. To address this, we introduce a rollout loss that penalizes drift at the final step, encouraging self-correcting trajectories and stabilizing long-range flow integration. We further propose a conditioning module that fuses audio and visual cues before vector field regression, enabling explicit cross-modal source selection. Extensive quantitative and qualitative evaluations show that our method consistently surpasses the previous state-of-the-art discriminative approach, establishing that visually-guided audio remixing is best addressed through generative modeling.

eess.AS↗