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arxiv: 2606.06962 · v1 · pith:B46J6RDAnew · submitted 2026-06-05 · 📡 eess.AS

FSC-Net: Integrating Fast Fourier Convolutions and Progressive Learning for Speech Bandwidth Extension

Xinan Chen , Xiaobin Rong , Qinwen Hu , Kai Chen , Jing Lu This is my paper

Pith reviewed 2026-06-27 21:12 UTC · model grok-4.3

classification 📡 eess.AS
keywords speech bandwidth extensionfast fourier convolutionsprogressive learningspectral mappingaudio qualityneural networksfrequency reconstruction
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The pith

FSC-Net reconstructs wideband speech from narrowband inputs by modeling full-spectrum frequency dependencies with fast Fourier convolutions and progressive learning.

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

The paper aims to improve speech bandwidth extension by reconstructing realistic high-frequency components from narrowband audio. It proposes FSC-Net, which incorporates fast Fourier convolutions to handle long-range interactions across the spectrum within a complex spectral mapping approach. A progressive learning strategy is used to build spectral details step by step from coarse to fine. This approach seeks to reduce artifacts in phase and harmonics that plague prior methods while keeping the model compact at 1.54 million parameters. If effective, it would enable higher quality audio upsampling with better generalization to new datasets.

Core claim

FSC-Net integrates Fast Fourier Convolutions into a complex spectral mapping framework to expand the receptive field across the entire spectrum and capture long-range frequency interactions. Combined with a frequency-progressive learning curriculum, the network addresses the ill-posed high-frequency generation problem by reconstructing details progressively from coarse to fine, leading to improved reconstruction quality and generalization on tasks like 4 kHz to 48 kHz upsampling.

What carries the argument

The integration of Fast Fourier Convolutions into the complex spectral mapping framework, which allows modeling of cross-band harmonic dependencies across the full spectrum.

Load-bearing premise

Integrating fast Fourier convolutions into the spectral mapping will expand the receptive field to the full spectrum and capture long-range interactions without creating new artifacts.

What would settle it

Experiments showing that on the VCTK 4 kHz-to-48 kHz task, FSC-Net does not attain the leading LSD and PESQ scores or introduces more artifacts than baselines.

Figures

Figures reproduced from arXiv: 2606.06962 by Jing Lu, Kai Chen, Qinwen Hu, Xiaobin Rong, Xinan Chen.

Figure 1
Figure 1. Figure 1: The general architecture of FSC-Net and the framework for progressive learning. The model consists of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Spectrogram comparison of different models on the VCTK dataset [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

Speech bandwidth extension (BWE) aims to reconstruct high-fidelity wideband audio from narrowband inputs. While recent approaches have made significant progress, they often struggle to reconstruct realistic high-frequency phase and harmonic structures, leading to perceptual artifacts. In this paper, we propose FSC-Net (Full-Spectrum Context Network), a parameter-efficient architecture designed to explicitly model cross-band harmonic dependencies. By integrating Fast Fourier Convolutions (FFCs) into a complex spectral mapping framework, FSC-Net expands its receptive field to the entire spectrum, capturing long-range frequency interactions effectively. To address the ill-posed nature of high-frequency generation, our novel frequency-progressive learning curriculum guides the network to reconstruct spectral details from coarse to fine. Experimental results on the VCTK and unseen EARS datasets demonstrate that FSC-Net delivers consistently strong reconstruction quality and generalization, particularly in the challenging VCTK 4 kHz-to-48 kHz task. Compared to scaled-up baselines, our model attains leading LSD and PESQ scores while maintaining a highly compact parameter footprint (1.54 M).

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.

Referee Report

1 major / 2 minor

Summary. The paper proposes FSC-Net, a compact (1.54 M parameter) architecture for speech bandwidth extension that integrates Fast Fourier Convolutions into a complex spectral mapping backbone to expand the receptive field across the full spectrum and employs a frequency-progressive learning curriculum to reconstruct high-frequency content from coarse to fine. It reports leading LSD and PESQ scores on the VCTK 4 kHz-to-48 kHz task and on the unseen EARS dataset relative to scaled baselines.

Significance. If the empirical results hold under rigorous verification, the work would demonstrate that FFC-based long-range frequency modeling combined with progressive training can deliver strong reconstruction quality and generalization in a highly parameter-efficient model. This addresses receptive-field limitations in spectral mapping and the ill-posedness of high-frequency generation, with potential value for real-time audio applications. The manuscript provides no machine-checked proofs or open code, but the explicit linkage of architectural choices to the reported metrics is a positive feature.

major comments (1)
  1. [Experiments] Experiments section: the central claim of leading LSD/PESQ scores on VCTK 4 kHz-to-48 kHz rests on point estimates without reported error bars, statistical significance tests, or explicit data-split and training-hyperparameter details; this information is required to assess whether the improvements over scaled baselines are reliable and reproducible.
minor comments (2)
  1. [Method] Method section: the precise placement of FFC layers within the complex spectral mapping U-Net (e.g., which encoder/decoder stages) is described at a high level; a diagram or equation showing the modified forward pass would improve reproducibility.
  2. [Introduction] Abstract and §1: the phrase 'scaled-up baselines' is used without naming the exact models or their parameter counts in the opening paragraphs; this should be clarified for immediate context.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the single major comment below and will revise the manuscript to strengthen the experimental reporting.

read point-by-point responses

  1. Referee: [Experiments] Experiments section: the central claim of leading LSD/PESQ scores on VCTK 4 kHz-to-48 kHz rests on point estimates without reported error bars, statistical significance tests, or explicit data-split and training-hyperparameter details; this information is required to assess whether the improvements over scaled baselines are reliable and reproducible.

    Authors: We agree that the current presentation relies on point estimates and that greater transparency is needed for reproducibility. In the revised manuscript we will: (1) provide explicit descriptions of the train/validation/test splits and any preprocessing steps, (2) list the complete set of training hyperparameters and optimization settings, and (3) report performance averaged over multiple random seeds together with standard deviations (error bars) and the results of appropriate statistical significance tests against the scaled baselines. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper is an empirical neural architecture proposal for speech bandwidth extension. It describes design choices (integrating FFCs into complex spectral mapping and a frequency-progressive curriculum) as addressing receptive-field and ill-posedness issues, then reports LSD/PESQ results on VCTK and EARS. No equations, derivations, or first-principles claims are present that reduce by construction to fitted parameters, self-citations, or renamed inputs. Performance claims rest on external experimental comparisons rather than any self-referential fitting or uniqueness theorem. The derivation chain is therefore self-contained against the reported benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the model is described at architectural level only.

pith-pipeline@v0.9.1-grok · 5726 in / 1010 out tokens · 16246 ms · 2026-06-27T21:12:48.957325+00:00 · methodology

discussion (0)

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Reference graph

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