Signal processing is one of the most important system control mechanisms across a wide variety of functional devices and mechanisms from electronics to biology. The chemical reaction networks underlying the response of a cell to both externally and internally generated signals comprise an extraordinary real-time multivariate control problem. There: are two phenomena that exemplify the biological importance of chemical systems' response to oscillatory signals. One includes a number of important cases of differential cellular response to particular frequencies of periodic chemical signals. The most widespread example of this is the encoding of an external agonist concentration in the frequency of calcium ion concentration spiking inside certain eukaryotic cells. The second is based on the fact that, owing to the low concentrations and slow reaction rates often associated with, for example, the mechanisms of gene expression, a significant amount of fluctuation in protein production rates is to be expected. Thus, mechanisms that are essential for the life of the cell must be robust to these and other types of random noise in the environment as well as be able to filter relevant signals from the background successfully. We analyze a number of commonly occurring chemical reaction networks, "motifs" or "modules", for their response to periodic single- and multifrequency signals. We find that even very simple chemical reaction networks can be selectively responsive to specific frequency ranges of the input signals. The main results are that first, a general system of linear reactions with a single external oscillatory input signal always acts as a low-pass frequency filter. With more than one input at the same frequency, the system can also be made to, behave as a band-pass filter in a selected range but never as a high-pass one. Second, a class of bimolecular reaction mechanisms can behave as a band-pass filter, but the behavior is very sensitive to the kinetic parameters. Third, a class of excitable chemical systems can act as a robust band-pass filter. These results also suggest methods for controlling system behavior through its response to oscillatory inputs, for deducing chemical reaction mechanisms, and for estimating the associated rate constants from measurements of system responses to frequency-variable perturbations.