The EKT method theoretical signal-to-noise ratio expression

The EKT method is a new extraction technique of periodic signals from noise. It is simply a cross-correlation of a periodic message with a reference signal obtained by summation of harmonics of the same amplitude. The only paper [J.S.A. Eyebe Fouda, M. Kom, A. Tiedeu, The EKT method for extraction of periodic signals from noise, Digital Signal Process. 16 (4) (2006) 343–357] published up to now on this method numerically shows that, for examples chosen on simulation, its signal-to-noise ratio (SNR) remains higher than that of the traditional method. However, practical calculation of SNR on some examples does not allow a user having other signals to know which is the best of the multitude methods for an extraction. Only the comparison of SNR literal expressions of the various methods can avoid it proceeding by groping. To this end, we will determine in this text, an expression for theoretical EKT method SNR gain.