I have a so-called "modified sine wave" inverter that is connected to 200+
amp hours of deep discharge battery located in about the center of the
house in the basement. About a 30-foot length of #14 wire goes to an
outlet box in the shack, down on one end of the house, and provides 110VAC
(of a sort) when the power is off and I don't feel like hauling out the
generator. :-)

Trouble is, whenever I turn on the inverter it spews harmonics all up and
down the HF band and makes it difficult to impossible to hear weak signals.

I realize that a pure sine wave inverter would mostly alleviate this but
that's not gonna happen any time soon... meanwhile is there a filter I can
apply to the output of the inverter to round off the corners of the
modified sine wave (which is really nothing but a stairstep square wave)
and eliminate the worst of the harmonic noise?

Thanks...