and is approximately equal to the required DC bias for BTN and PL. However, when $0.420\le \alpha < 1$, the required DC bias starts to fluctuate slightly around $\mu=0.25\hat{a}$ and the minimum happens for $\alpha =0.715$. The reason for this behavior is that in RRC, the peak is a function of $\alpha$, see Table \[pulse-def\]. As a result, by increasing the roll-off factor, there will be a compromise between the reduction in the sidelobe amplitude and the increase in peak amplitude. For small values of $\alpha$, the sidelobe reduction is more significant than the peak increase, and as a result, the required DC bias decreases. The Xia pulse always requires the largest DC bias. For $0< \alpha \le 0.730$, similar to other pulses, by increasing the roll-off factor, the required DC bias for Xia pulses decreases. However, when $0.730\le \alpha < 1$, the required DC bias starts to fluctuate slightly and starts to approach the required DC for RRC.

The expression for $\mu$ given in (\[eq:DC\]) illustrates the reason why the double-jump and sinc pulses are not considered in Sec. \[sec:Pulse-shaping\]. These pulses decay as $1/|t|$. As a result, the summation in (\[eq:DC\]) does not converge to a finite value. 