Extracting hidden weak sinusoidal signal with short duration from noisy data: Analytical theory and computational realization

Zhang Ying¹, Zhang Zhaoyang^{1, 2}, Qian Hong³, Hu Gang^{1, †}

(color online) The same as Fig. 2 with formula of Eqs. (5), (11), and (14) (continuous curves) and numerical results of Eq. (10) (dots) applied. Parameters of the filter Eq. (8) are given as: , , and . The input I(t) in Fig. 2 is replaced by the output of Eq. (8).