Cells decode information of signaling activation at a scale of tens of minutes by downstream gene expression with a scale of hours to days, leading to cell fate decisions such as cell differentiation. However, no system identification method with such different time scales exists. Here we used compressed sensing technology and developed a system identification method using data of different time scales by recovering signals of missing time points. We measured phosphorylation of ERK and CREB, immediate early gene expression products, and mRNAs of decoder genes for neurite elongation in PC12 cell differentiation and performed system identification, revealing the input-output relationships between signaling and gene expression with sensitivity such as graded or switch-like response and with time delay and gain, representing signal transfer efficiency. We predicted and validated the identified system using pharmacological perturbation. Thus, we provide a versatile method for system identification using data with different time scales.