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) Bar charts of signal detection results on ten groups of experiments of Figs. 6(c) and 6(d) and Figs. 7(c) and 7(d). Each group performs 1000 realizations of numerical computations of Eq. (3) (the input: (a) for A = 0, (b) for A = 0.006) and Eq. (10) (the output: (c) for A = 0, (d) for A = 0.006). Numbers of correct (red) and error (black) detections are ranged. It is obvious that with the optimal resonant filter more realizations move to the correct side than those moving to the wrong side (panels (e) and (f)).