{'fraction_non_alphanumeric': 0.020674646354733407, 'fraction_numerical': 0.0, 'mean_word_length': 5.258503401360544, '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}}
Gabor transform of time-varying systems: exact representation and approximation

Approximate modeling of discrete-time linear time-varying systems is studied based on a representation of linear systems in the Gabor time-frequency space. The time-varying system is assumed to be given in input-output or kernel representation. This representation has previously received attention because of its applicability in frozen-time analysis and design of optimal control for time-varying systems but requires a large number of coefficients. Motivated by its application to signal analysis, the Gabor transform is considered as a tool for the representation and approximation of linear time-variant systems. In order to show the main results, the class of systems considered is restricted to the one usually considered in the frozen-time approach. An example is included to illustrate the potential application of the technique.