Quantum Interpretation of Frequency Operator

The frequency operator of signal is obtained in this paper. It reflects the quantum characteristics of signal. It is a linear and Hermitian operator. Eigenfunctions, eigenvalues and superposition principle of signal are researched by using the frequency operator. The frequency operator is used to prove the uncertainty principle of signal. The uncertainty principle of signal indicates that the signal can be considered as a kind of the quasi quantum system with wave-particle dualism. The frequency operator is a powerful tool to research the quantum characteristics of signal. The quantum interpretation of frequency operator explains the essence of signal and provides the theory support for applying the framework of quantum mechanics to the signal processing.