Frame bounds and bandwidth tiling for time-causal bandpass wavelets
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.
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BibTeX
@misc{pedersen2026frame,
title = {{Frame bounds and bandwidth tiling for time-causal bandpass wavelets}},
author = {Jens E. Pedersen and Tony Lindeberg and Peter Gerstoft},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17201},
eprint = {2609.17201},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17201},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Frame bounds and bandwidth tiling for time-causal bandpass wavelets
AU - Jens E. Pedersen
AU - Tony Lindeberg
AU - Peter Gerstoft
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.17201
UR - https://arxiv.org/abs/2609.17201
AB - 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.
ER -