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) Schematic figures of signal detection tasks. (a) Direct signal detection from the input I(t). (b) Signal detection from the output of a selected linear filter driven by the input I(t). The central problem is: whether the latter analysis can out-perform the former signal detection directly from the input.