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.

  1. 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.
  2. Robinson, E. A., 1963b, Extremal properties of the Wold decomposition: Journal of Mathematical Analysis and Applications, 6, 75–85.