Climate signals are the results of interactions of multiple timescale media such as the atmosphere and ocean in the coupled earth system. Coupled data assimilation (CDA) pursues balanced and coherent climate analysis and prediction initialization by incorporating observations from multiple media into a coupled model. In practice, an observational time window (OTW) is usually used to collect measured data for an assimilation cycle to increase observational samples that are sequentially assimilated with their original error scales. Given different timescales of characteristic variability in different media, what are the optimal OTWs for the coupled media so that climate signals can be most accurately recovered by CDA? With a simple coupled model that simulates typical scale interactions in the climate system and twin CDA experiments, we address this issue here. Results show that in each coupled medium, an optimal OTW can provide maximal observational information that best fits the characteristic variability of the medium during the data blending process. Maintaining correct scale interactions, the resulting CDA improves the analysis of climate signals greatly. These simple model results provide a guideline for when the real observations are assimilated into a coupled general circulation model for improving climate analysis and prediction initialization by accurately recovering important characteristic variability such as sub-diurnal in the atmosphere and diurnal in the ocean.