Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: Novo Nordisk, Vetenskapsrådet
OpenAlex ID: W7213558619