发表机构
Technical University of Denmark; KTH Royal Institute of Technology（丹麦技术大学; 瑞典皇家理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对时间因果带通小波，推导了闭式框架界与条件数，给出尺度比和通道数的设计规则，并通过递归滤波器离散实现验证，保障流式信号表示的可靠性。
AI 中文摘要
为信号表示提供强有力保证的小波和框架是信号处理理论的基石，但长期以来仅限于非因果设置。近期工作将小波分析扩展到处理流式信号的时间因果系统，具备精确重构和时间递归实现。然而，使此类表示在噪声和量化下可靠的框架保证尚未被刻画。我们推导了时间因果带通小波在带限域、峰值频率、常数Q带宽铺砌和频谱衰减率上的闭式框架界及条件数。我们的工作为尺度比和通道数提供了设计规则，并通过因果小波的递归滤波器离散实现进行了数值验证。
英文摘要
Wavelets and frames that provide strong guarantees for signal representations are a cornerstone in signal processing theory, but have long been restricted to non-causal settings. Recent work extended wavelet analysis to time-causal systems that operate on streaming signals, with exact reconstruction and time-recursive implementations. However, the frame guarantees that make such representations reliable under noise and quantization are uncharacterized. We derive closed-form frame bounds and conditioning on band-limited domains, together with peak frequencies, constant-Q bandwidth tiling, and spectral decay rates for time-causal bandpass wavelets. Our work provides design rules for the scale ratio and channel count, which we validate numerically against discrete implementations of the causal wavelets in terms of recursive filters.
