{'fraction_non_alphanumeric': 0.022388059701492536, 'fraction_numerical': 0.0, 'mean_word_length': 5.643564356435643, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Unified theory of time-sequential sampling

We consider the sampling of band-limited spatio-temporal signals subject to the time- sequential (TS) constraint that only one spatial sample can be taken at a given time. Using the powerful techniques of lattice theory, we develop a new unifying theory linking TS sampling with generalized multidimensional sampling. The theory, which applies to arbitrary spatial and spectral supports in any dimension, includes tight fundamental performance bounds, which are asymptotically achievable. Simple graphical design algorithms are provided for lattice sampling patterns minimizing the sampling rates, and illustrated by examples.