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The resonant transfer process is extended to include greater generality. This leads to certain new applications. Baseband-to-baseband resonant transfer transmission has been used for a number of years in the area of time division switching. In addition, recently the more general concept of single-sideband-tosingle-sideband transmission, which would include the baseband-tobaseband case, has been used to obtain frequency division multiplexing. This technique allows time division switching and frequency division multiplexing to be combined into one common operation. Such an integrated system has been labeled integrated switching and multiplexing (ISAM). In this paper, the generality is carried one step further. The restriction that the input and output resonant transfer filters each cover a single-sideband frequency region has been removed. Instead, the filters are allowed to cover one or more such regions. This leads to the concept of lossless resonant transfer transmission between filters of unequal bandwidth. The reason for considering this is that several applications involving this type of operation have become apparent. Two of the more important of these applications have to do with the insertion of signaling information into the ISAM system and with establishing conferencing connections within the system. This new mode of resonant transfer transmission is rigorously analyzed and the applications discussed. These techniques are equally applicable to conventional basebandto-baseband time division switching.