# Translations:Appendix N: The energy-delay theorem/30/en

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This equation is the energy-delay theorem (Robinson, 1963a^{[1]}, 1963b^{[2]}). It says that if the same input is applied to both a minimum-delay filter and any other stable causal filter with the same amplitude spectrum, then the partial energy of the output of the minimum-delay filter is greater than or equal to the partial energy of the output of the other filter. In other words, a minimum-delay filter produces less energy delay than does any other causal filter with the same amplitude spectrum. This theorem is the reason for the use of the term *minimum delay*, referring to the fact that a minimum-delay filter delays the energy the least.

- ↑ Robinson, E. A., 1963a, Nekotorye svoystva razlozheniya vol’da statsionarnykh sluchaynykh protsessov [Properties of the Wold decomposition of stationary stochastic processes (in Russian)]: Teoriya Veroyatnostei i ee Primememiya, Akademiya Nauk SSSR,
**7**, no. 2, 201–211. - ↑ Robinson, E. A., 1963b, Extremal properties of the Wold decomposition: Journal of Mathematical Analysis and Applications,
**6**, 75–85.