Realizable Ideal D/C and C/D Conversions for Band-Limited Periodic Signals and Characterization of Single-Carrier Block Transmission

For a real band-limited periodic signal, there are reconstruction formulas that realize the ideal discrete-to-continuous (D/C) conversion within one period of the signal. However, the previous results may not be suitable for general complex band-limited periodic signals. For complex band-limited periodic signals, in this paper we first propose the reconstruction formulas, which lead to realizable forms of ideal D/C conversion. We then derive the correlation function of the interpolation pulse, and this helps us construct a matched filter that can implement the exact sampling (C/D conversion) of a complex band-limited periodic signal. When there exists noise in the sampling process, comparing with the ideal impulse sampling, the proposed C/D conversion can maintain finite output noise variance. The correlation function of the output noise is also given, and the oversampling effect of noise is analyzed. For a complex interpolation pulse, in general we cannot decouple the ideal D/C (or C/D) conversion into two independent D/C (or C/D) conversions for the real and imaginary parts of the signal. We also give the extended forms and decomposition forms of the proposed D/C and C/D conversions. Our results are applied to derive the ideal D/C and C/D conversions in the precoded orthogonal frequency-division multiplexing (POFDM) system. The resulted interpolation pulses are used to characterize the single-carrier (SC) block transmission under the POFDM architecture. We give characteristics that distinguish the SC block transmission from traditional SC transmission.