An effective theoretical analysis method is presented to analyze different linear optical signal processing functions with optical filters reported in literatures. For different applications, the optical filters are supposed to operate on the analog or digital part of the signal separately, namely analog spectrum conversion and digital spectrum conversion. For instance, the return-to-zero (RZ) to non-return-to-zero (NRZ) format conversion for intensity or phase modulated signals are based on the analog spectrum conversion process, while the (N)RZ to (N)RZ phase-shift-keying (PSK) format conversion, logic NOT gate and clock recovery for RZ signals are based on the digital spectrum conversion process. Theoretical analyses with the help of numerical simulation are used to verify the reported experimental results, and all the experimental results can be effectively analyzed with this analytical model. The effect of the transmission spectrum of the filter on the performance of the converted signal is investigated. The most important factor is that the theoretical analysis provides an effective way to optimize the optical filter for different optical signal processing functions.