{'fraction_non_alphanumeric': 0.021413276231263382, 'fraction_numerical': 0.004282655246252677, 'mean_word_length': 5.404109589041096, '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}}
Improved frequency marginal estimates for time-frequency distributions

Time-frequency distributions (TFDs) are used for representing the energy density of a signal simultaneously in time and frequency. The frequency marginal is defined as the density of frequency at a particular time. When the frequency marginal is satisfied, it is given by the classical periodogram formulation. In spectral estimation literature, the periodogram is not considered to be a good spectral estimate because of the high variance it exhibits. For this reason, several modified periodogram methods including Thomson's (1982) spectral estimation method have been introduced. In this paper, a new kernel design method to obtain a smoothed spectrum as the frequency marginal is introduced. The necessary conditions on the time-frequency kernel are derived. The consequences of this new kernel design method in signal analysis are illustrated with examples.