This article is devoted to the improvement of signal recognition methods based on information characteristics of the spectrum. A discrete function of the normalized ordered spectrum is established for a single window function included in the discrete Fourier transform. Lemmas on estimates of entropy, imbalance, and statistical complexity in processing a time series of independent Gaussian variables are proved. New concepts of one- and two-dimensional spectral complexities are proposed. The theoretical results were verified by numerical experiments, which confirmed the effectiveness of the new information characteristic for detecting a signal mixed with white noise at low signal-to-noise ratios.

The paper is devoted to the study of information characteristics which play an important role in solving problems of detection of weak signals and their classification. We formulate and prove lemmas on estimating upper and lower boundaries in statistical and spectral complexity diagrams for different signal-noise mixtures. The obtained theoretical results are verified by numerical experiments, which have confirmed the efficiency of the theoretical estimates. We establish some important laws of the behavior of noise-like and weak signals and the possibilities of their detection in white and blue noise conditions, formulate and prove the corresponding lemmas. Also, we obtain estimates on conditions for the possibility of classifying weak signals by means of information characteristics.

The paper considers the problem of detecting and classifying acoustic signals based on information (entropy) criteria. A number of new information features based on time-frequency distributions are proposed, which include the spectrogram and its upgraded version, the reassigned spectrogram. To confirm and verify the proposed characteristics, modeling on synthetic signals and numerical verification of the solution of the multiclass classification problem based on machine learning methods on real hydroacoustic recordings are carried out. The obtained high classification results ($F1=0.95$) allow us to assert the advantages of using the proposed characteristics.

This article is devoted to the improvement of signal recognition methods based on the information characteristics of the spectrum. A discrete function of the normalized ordered spectrum is established for a single window function included in the DFT. Lemmas on estimates of entropy, imbalance and statistical complexity in processing a time series of independent Gaussian quantities are proved. New concepts of one-dimensional and two-dimensional spectral complexities are proposed. The theoretical results obtained were verified by numerical experiments, which confirmed the effectiveness of the new information characteristic when detecting a signal mixed with white noise at low signal-to-noise ratios.

An addition to the article “A new spectral measure of complexity and its capabilities for detecting signals in noise” is presented.

Представлено исследование диаграмм статистической и спектральной сложности, которые играют важную роль в решении задач обнаружения слабых сигналов, их классификации. Сформулированы и доказаны леммы об оценке верхней и нижней границ на диаграммах статистической и спектральной сложностей для различных сигнально-шумовых смесей. Полученные теоретические результаты верифицированы численными экспериментами, которые подтвердили эффективность теоретических оценок.