A signal processing system includes a signal processing device including a processor and a memory device storing first information and a signal transmitting device including a memory device storing second information. The processor reads the memory devices to obtain the first information and the second information, determines a threshold date according to a first date indicated by the first information and a margin, and determines whether a second date indicated by the second information is earlier than the threshold date. When the second date is earlier than the threshold date, the processor controls the signal processing device to operate in a limited mode. In the limited mode, the signal processing device does not output any signal to the signal transmitting device or ignores any signal from the signal transmitting device, or the signal processing device only outputs a limited signal to the signal transmitting device.