Peak Magnitude of Oversampled Trigonometrie Polynomials

The theory of trigonometric polynominals has attracted new attention with the application of polynomials to multicarrier communication systems (OFDM, DMT, MC-CDMA). It is also well-known that polynominals have been successfully applied to system identification. Following the classical theory these signals can be described by sampling sets such that there is a unique relation between the samples and the polynominals. However, it is a problem in many applications that the peak magnitude of the samples does not indicate the peak magnitude of the polynominal. For example amplifier clipping in multicarrier systems leading to performance degradation is caused by the continuous signals whereas the signal is digitally generated and processed. This paper addresses this problem and introduces the method of oversampling in order to relate the peak magnitudes of the polynominal and the samples. In particular, a practical formula is derived in order to trade off signal processing effort for performance. This formula improves a result given by [1,2].