This work presents the proof of concept of using energy operator theory based on the conjugate Teager-Kaiser energy operators in matched filters for signal detection in multipath fading channels. To do so, we consider signals in the space $\mathcal{S}(\mathbb{R})$ a subspace of the Schwartz space $\mathbf{S}^-(\mathbb{R})$ in order to approximate the received signal. These functions obey to some specific properties as shown in this work. It allows to decompose the received signals into subchannels with their own Signal-to-Noise-Ratio.