{'fraction_non_alphanumeric': 0.010917030567685589, 'fraction_numerical': 0.006550218340611353, 'mean_word_length': 5.0394736842105265, '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}}
A generalization of raised cosine pulses

An investigation was carried out in order to decipher the mechanism behind the increased performance of the improved Nyquist filter when sampled with a time offset, as compared with the classical raised cosine filter. A family of generalized raised cosine filters was introduced and its performance was investigated in terms of probability of error. Exact formulae of the impulse response were derived for n=1 to 22.