In this paper, we investigate the issue of pulse propagation in a fragmented spectrum (FS) and adaptive equalization using embedded probing signals via feed forward paths only. A novel wavefront (WF) multiplexing (Muxing) and de-multiplexing (Demuxing) scheme as a pre- and post- processing method is proposed for wideband waveforms or data symbols propagation through non-contiguous (NC) frequency slots in an FS. Embedded probing signals as a part of the input to the WF Muxing processor are used for diagnostic as a part of an equalization procedure. The performance of this scheme is evaluated via simulations. The results show pulse distortions can be minimized by equalizing propagation effects of NC channels via the WF Muxing and Demuxing techniques.