title: ÐÑÐµÐ½ÐºÐ¸ ÑÐ°Ð·Ð¾Ð²Ð¾Ð³Ð¾ ÑÐ´Ð²Ð¸Ð³Ð° Ð¸ ÑÑÐ½ÐºÑÐ¸Ð¹ ÐºÐ¾Ð³ÐµÑÐµÐ½ÑÐ½Ð¾ÑÑÐ¸ Ð² Ð·Ð°Ð´Ð°ÑÐ°Ñ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° ÑÑÐ¾Ñ Ð°ÑÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ²ÑÐ·ÐµÐ¹ ÐºÐ²Ð°Ð·Ð¸Ð¿ÐµÑÐ¸Ð¾Ð´Ð¸ÑÐµÑÐºÐ¸Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð²
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Estimates of the phase shift and coherence function in the problems of analyzing stochastic relationships of quasiperiodic time series
Creators: name: ÐÑÑÐ½Ð¾ÑÐ¾Ð², ÐÐ¼Ð¸ÑÑÐ¸Ð¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2020
Subjects: ÐºÐ¾ÑÑÐµÐ»ÑÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÑÐ½ÐºÑÐ¸Ñ
ÑÑÐ½ÐºÑÐ¸Ñ ÐºÐ¾Ð³ÐµÑÐµÐ½ÑÐ½Ð¾ÑÑÐ¸
ÐºÑÐ¾ÑÑ-ÑÐ¿ÐµÐºÑÑÐ°Ð»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð·
Ð¼ÐµÑÐ¾Ð´ Ð¿ÐµÑÐ¸Ð¾Ð´Ð¾Ð³ÑÐ°Ð¼Ð¼ ÑÑÐ»ÑÐ°
correlation function
coherence function
cross-spectral analysis
welch's method

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð² Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐ¿ÐµÐºÑÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¸ ÐºÑÐ¾ÑÑ-ÑÐ¿ÐµÐºÑÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°. Ð Ð°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÐµ Ð¿Ð¾Ð½ÑÑÐ¸Ñ, Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¸ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ ÐºÑÐ¾ÑÑ-ÑÐ¿ÐµÐºÑÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°, Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼ÑÐµ Ð´Ð»Ñ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹. Ð Ð°Ð±Ð¾ÑÐ° Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð° Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ñ SciPy Ñ Ð¾ÑÐºÑÑÑÑÐ¼ ÐºÐ¾Ð´Ð¾Ð¼, Ð¾Ð±Ð»Ð°Ð´Ð°ÑÑÐ¸Ð¼ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼ÑÐ¼Ð¸ Ð² ÑÐ°Ð¼ÐºÐ°Ñ Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ°Ð¼Ð¸. ÐÐ°Ð´Ð°ÑÐ¸, ÑÐµÑÐ°ÐµÐ¼ÑÐµ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ: 1. ÐÐ¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ Ð¾ÑÐµÐ½Ð¾Ðº ÐºÐ¾Ð³ÐµÑÐµÐ½ÑÐ½Ð¾ÑÑÐ¸ Ð´Ð»Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð² Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð° Ð¿ÐµÑÐ¸Ð¾Ð´Ð¾Ð³ÑÐ°Ð¼Ð¼ Ð£ÑÐ»ÑÐ° Ð¸ Ð°Ð¿Ð¿Ð°ÑÐ°ÑÐ° ÐºÑÐ¾ÑÑ-ÑÐ¿ÐµÐºÑÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°. 2. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ°Ð·Ð¾Ð²ÑÑ ÑÐ´Ð²Ð¸Ð³Ð¾Ð² ÐºÐ°Ðº Ð²Ð½ÑÑÑÐ¸ Ð¾ÑÐ´ÐµÐ»ÑÐ½Ð¾Ð³Ð¾ ÑÑÐ´Ð°, ÑÐ°Ðº Ð¸ Ð¼ÐµÐ¶Ð´Ñ Ð´Ð²ÑÐ¼Ñ ÑÑÐ´Ð°Ð¼Ð¸. 3. ÐÑÐµÐ½ÐºÐ° ÑÑÐµÐ¿ÐµÐ½Ð¸ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐ²ÑÐ·Ð½Ð¾ÑÑÐ¸ Ð´Ð²ÑÑ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð¾Ð² Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ð¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð½ÑÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÑÑ ÑÐµÐ°Ð»ÑÐ½ÑÐµ Ð´Ð°Ð½Ð½ÑÐµ, Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÑÑÐ¸Ðµ ÑÐ¾Ð±Ð¾Ð¹ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¾Ð²ÑÐ¹ ÑÐ¸Ð³Ð½Ð°Ð», Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¹ Ñ Ð´Ð°ÑÑÐ¸ÐºÐ°, Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´ÑÑÐµÐ³Ð¾ Ð·Ð°Ð¼ÐµÑÑ Ð°ÑÑÐµÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð´Ð°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¸ ÑÐºÐ¾ÑÐ¾ÑÑÐ¸ ÐºÑÐ¾Ð²Ð¾ÑÐ¾ÐºÐ°. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð¼ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ²Ð»ÑÑÑÑÑ Ð²ÑÐ²Ð¾Ð´Ñ Ð¾ Ð½Ð°Ð»Ð¸ÑÐ¸Ð¸ ÑÑÐ¾ÑÐ°ÑÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ²ÑÐ·ÐµÐ¹ Ð² Ð¸ÑÑÐ»ÐµÐ´ÑÐµÐ¼ÑÑ Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÑÐ´Ð°Ñ.
description: This work is devoted to the study of time series using spectral and cross-spectral analysis methods. The basic concepts, models and cross-spectral analysis algorithms necessary for research are considered. The work was performed using open-source SciPy mathematical software that has the necessary tools as part of the task. Tasks solved in the course of work: 1. Construction of coherence estimates for time series using the Welch periodogram method and the cross-spectral analysis apparatus. 2. The study of phase shifts both within a single row and between two rows. 3. Assessment of the degree of linear connectivity of two time series based on the results of studies. The work uses real data, which is an analog signal received from a sensor on a personâs body that measures blood pressure and blood flow velocity. The result of the study is the conclusion about the presence of stochastic relationships in the studied time series.