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.