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Equivalance of Time-Multiplexed and Frequency-Multiplexed Signals in Digital Communications

In comparing different techniques for multiplexing N binary data signals into a single channel, time-division multiplexing (TDM) is known to have a theoretic efficiency of 100 percent (neglecting sync power) and thus seems to outperform frequencydivision multiplexing systems (FDM). By considering more general FDM systems, we will show that both TDM and FDM are equivalent and have an efficiency of 100 percent. The difference between the systems is in the multiplexing and demultiplexing subsystems, but not in the performance or in the generated waveforms.