A sampling theorem for periodic functions with no minus frequency component and its application

The sampling theorem of Whittaker, Ogura, Kotelnikov, Someya, and Shannon (WOKSS´s sampling theorem) appears in most books on information theory, and is well known. WOKSS´s sampling theorem must exclude periodic functions. This paper first introduces a sampling theorem for periodic functions, and gives its physical meaning; this theorem is effective for functions that can be expressed as a finite Fourier series in the same way as WOKSS´s theorem deals with a band-limited signal. Since many signals such as an Orthogonal Frequency Division Multiplexing (OFDM) signal can be expressed by periodic functions, the sampling theorem can play an important role in a communications area. Extending the theorem, this paper proposes a sampling theorem for periodic functions with no minus frequency component of a finite Fourier series, and shows its example. In addition, we examine the OFDM signal generation and termination by applying sampling theorems for periodic functions including the proposed one.