Analytic Method for the Computation of the Total Harmonic Distortion by the Cauchy Method of Residues

The total harmonic distortion (THD) is an important performance criterion for almost any communication device. In most cases, the THD of a periodic signal, which has been processed in some way, is either measured directly or roughly estimated numerically, while analytic methods are employed only in a limited number of simple cases. However, the knowledge of the theoretical THD may be quite important for the conception and design of the communication equipment (e. g. transmitters, power amplifiers). The aim of this paper is to present a general theoretic approach, which permits to obtain an analytic closed-form expression for the THD. It is also shown that in some cases, an approximate analytic method, having good precision and being less sophisticated, may be developed. Finally, the mathematical technique, on which the proposed method is based, is described in the appendix.