Finite Duration Root Nyquist Pulses with Maximum In-Band Fractional Energy

We design root Nyquist pulses having maximum in-band fractional energy for a given finite bandwidth. The problem of maximizing the ratio of in-band energy to total energy has been dealt with earlier. But an exact solution could not be found since it involved optimization of a quadratic objective function with quadratic constraints. We have found an exact solution to this problem by taking a different approach. Numerical results are presented comparing the pulses so obtained with the raised cosine pulse and the better than raised-cosine (BTRC) pulse.