{'fraction_non_alphanumeric': 0.010767160161507403, 'fraction_numerical': 0.0, 'mean_word_length': 5.702702702702703, '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}}
The lifting theorem and the design of biorthognal filter banks

In this paper, a simple design method is proposed for the construction of biorthogonal filter banks with perfect reconstruction property. Starting from an analysis filter bank that meets certain design specifications regarding bandwidth and energy concentration, a complete biorthogonal filter bank system is constructed. Then, through applying the lifting scheme to the other analysis filter bank, its response can be greatly improved to meet the desired design specifications without impairing either the perfect construction property or the other analysis filter bank. Illustrative example is given to demonstrate the simplicity and efficiency of the proposed design approach.