Embodiments include processes, systems, and devices for reshaping virtual baseband signals for transmission on non-contiguous and variable portions of a physical baseband, such as a white space frequency band. In the transmission path, a spectrum virtualization layer maps a plurality of transmission components associated with a transmission symbol produced by a physical layer protocol to sub-carriers of the allocated physical frequency band. The spectrum virtualization layer then outputs a physical transmission symbol composed of time-domain samples derived from the mapped frequency components and a cyclic prefix. In the receive path, a time-domain symbol received on the physical baseband is reshaped and equalized by the virtual spectrum layer in order to recompose a time-domain samples of a transmission stream in the virtual baseband.