{'fraction_non_alphanumeric': 0.009070294784580499, 'fraction_numerical': 0.0, 'mean_word_length': 4.972972972972973, '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}}
Sampling and interpolation in two dimensions

The aim of this paper is to consider the interpretation of limited data sets to represent functions which are bandlimited. It is shown that limited data leads to a degree of non-uniqueness of interpolation and extrapolation that only the imposition of a priori constraints can reduce. An approach is described to enable a priori information to be incorporated in a Fourier reconstruction scheme.