Gram-Schmidt Orthogonalization Procedure

In Digital communication, we apply input as binary bits which are converted into symbols and waveforms by a digital modulator. These waveforms should be unique and different from each other so we can easily identify what symbol/bit is transmitted. To make them unique, we apply Gram-Schmidt Orthogonalization procedure. Now consider that we have a waveform \(s_1(t)\) and we assume that its energy is \(\varepsilon_1\). Then we can construct our first waveform as: \(\begin{equation} \psi_1(t) = \frac{s_1(t)}{\sqrt{\varepsilon_1}} \label{energy_1} \end{equation}\) So now we have our first waveform which has energy = 1. Now we have our second waveform available known as...