A broadband digital communication network transmits a signal with a shaped power spectrum to minimize interference with devices that share the communication medium. In one embodiment using coaxial wiring, devices such as cable converters and televisions that are not part of the network share the communication medium and are exposed to the network signal. Power levels across the network band are selected to reduce interference in the non-networked devices. One area of susceptibility is the tuner of cable channel receivers, which perform mixing and down conversion of RF signals. The power spectrum profile is selected to minimize the IF and base band interference after down conversion. The spectrum can be shaped within each 6 MHz band to further minimize the interference with a TV signal. The power levels can be optimized for both peak power limitation and quantization effects.