Abstract—When any arbitrary number of sinusoids with same frequency but different amplitudes and phases are added together, the resultant sinusoid has the same frequency. We derive a closed form expression and provide two different approaches to prove the theorem.

Index Terms—Harmonic addition theorem, phasor addition theorem, phasor addition rule

Nay Oo is with the Department of Hearing, Speech and AudioTechnology (HSA), Fraunhofer Institute for Digital Media Technology(IDMT), Oldenburg, Germany (e-mail: nay.oo@idmt.fraunhofer.de)
Woon-Seng Gan is with School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore.

Cite: Nay Oo and Woon-Seng Gan, "On Harmonic Addition Theorem," International Journal of Computer and Communication Engineering vol. 1, no. 3, pp. 200-202 , 2012.