Thorough spectral investigation of the β-α pulse shaping filter

The β-α pulse shaping filter was proposed and investigated as a solution to decrease the PAPR over a SC-FDMA transmission system. In the present paper it is derived the frequency characteristic of the β-α filter as a closed-form expression to be used in an analysis regarding its use as an improved Nyquist filter. We evidenced the fact that the β-α filter is obtained from the convolution of an ideal rectangular filter with an RC filter having an increased excess bandwidth αβ and determined a condition that must be satisfied in order to have a real filter with even-symmetry around zero frequency.