On The Equivalence of Time-Division and Frequency-Division Multiplexing

On the basis of a general sampling formula it is shown that, for a system of
n
band-limited signals, FDM and band-limited TDM are equivalent in the sense that one can be derived from the other by a simple linear transformation. The transformation matrix is the same as for expanding an arbitrary polyphase system with
n
phases into its symmetric components. It is further shown that this equivalence also holds for nonideal sampling waveforms as they appear in certain multiplexing and demultiplexing systems used in practice.