Facsimile signature refers to a signature affixed by a special machine at the owner’s order.
Example of a state statute (Ohio) defining facsimile signature
ORC Ann. 9.10 Definition of facsimile signature
"facsimile signature" includes, but is not limited to, the reproduction of any authorized signature by a copper plate or by a photographic, photostatic, or mechanical device, but does not authorize the use of a rubber stamp signature by the official or authorized employee referred to in section 9.11 of the Revised Code on the face of any instrument mentioned in such section.