What's the rationale behind this pulse shaping function? Section 13.2 of the HD Radio standard for AM defines a pulse shaping function that appears to be some strange variant on a raised cosine filter:





More specifically, H(ξ) is a raised cosine filter with total width (1+α)T, and W(ξ) appears to be a "stretched" version. Why do they do this?
The pulse envelope is convolved with a Gaussian function to soften the transition between the symbols. If the standard pulse envelope were used without any softening, it would be audible to an AM detector (it runs at ~172 Hz).

Source: The IBOC Handbook: Understanding HD Radio (TM) Technology by David P. Maxson