In 1949, José Enrique Moyal, who had derived it independently, recognized it as the quantum moment-generating functional, and thus as the basis of an elegant encoding of all quantum expectation values, and hence quantum mechanics, in phase space (see Phase-space formulation). It has applications in statistical mechanics, quantum chemistry, quantum optics, classical optics and signal analysis in diverse fields, such as electrical engineering, seismology, time–frequency analysis for music signals, spectrograms in biology and speech processing, and engine design.