{'fraction_non_alphanumeric': 0.011320754716981131, 'fraction_numerical': 0.0, 'mean_word_length': 5.862068965517241, '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}}
Application and numerical implementation of fractional calculus to digital watermark

The paper mainly concerns and studies the application and implementation of fractional calculus to digital watermark algorithm. In the first, it discusses how to implement fractional calculus pseudo-random sequence by the sampling deviation of fractional calculus sinusoidal signal. In addition, it puts forward a fractional calculus based digital watermark algorithm, the security of which depends on the unknown of fractional orders and initial phrases. In the last, it proves the imperceptibility and robustness of this algorithm by simulation experiment, and shows that whether the embedded digital watermark sequence is extracted completely depends on the awareness of fractional order and initial phrase