Pitch Smoothing Using Relative Interval Networks

2026-09-30

AI Summary

This study addresses the limitations of conventional pitch smoothing, which lacks long-range perceptual awareness and remains susceptible to octave errors. To overcome these issues, this work proposes a relative interval network that leverages the variable-Q transform to extract multi-hop pitch differences, thereby transcending first-order continuity constraints. By introducing data-driven multi-hop relative interval constraints, the proposed method reformulates trajectory smoothing as a minimum-cost circulation problem optimized under the L1 norm, enabling efficient solutions. Experimental results demonstrate that this approach substantially enhances the performance of weak estimators, achieving accuracy comparable to or exceeding that of Viterbi decoding while exhibiting superior robustness under acoustically degraded conditions.

Abstract

Pitch tracking systems typically couple a per-frame fundamental frequency ($F_0$) estimator with a temporal smoothing stage to obtain continuous trajectories. Conventional Viterbi smoothers enforce first-order continuity but lack long-term temporal awareness and could lock into octave errors across corrupted frames. We propose Relative Interval Networks (RIN), a trajectory smoothing framework that reconciles per-frame pitch estimates with data-driven multi-hop pitch differences. We extract robust relative pitch intervals across arbitrary frame offsets using Variable-Q Transform cross-correlation. We formulate pitch smoothing as an $L_1$-norm optimization problem and prove its equivalence to a minimum cost circulation problem, solved efficiently via linear programming. Evaluations across speech, singing, and instrumental datasets show that RIN substantially improves weak estimators, matches or outperforms Viterbi decoding at a comparable computational cost, and provides superior robustness under certain acoustic degradation.

Problem

• pitch tracking
• pitch smoothing
• fundamental frequency estimation
• octave errors
• temporal continuity

Innovation

• Relative Interval Networks
• Pitch Smoothing
• Variable-Q Transform
• L1-norm Optimization
• Minimum Cost Circulation