Realizable Forms of Ideal D/C and C/D Conversions for Complex Bandlimited Periodic Signals

For real bandlimited periodic signals, the author of [2] proposed reconstruction formulas such that the ideal discreteto-continuous-time (D/C) conversion can be realized within one period of the signal. However, for general complex bandlimited periodic signals, the results of [2] cannot be directly applied to the real and imaginary parts of the signals. Furthermore, no corresponding ideal continuous-to-discrete-time (C/D) conversion has been proposed. In this paper, we first derive the reconstruction formulas for complex bandlimited periodic signals, and this leads to a realizable form of ideal D/C conversion. For the interpolation pulse of the D/C conversion, we construct its correlation function, based on which we further propose a matched filter that can implement the ideal sampling (C/D conversion) of a complex bandlimited periodic signal. We compare the sampling effect and noise effect of the proposed C/D conversion with other sampling approaches. When there are white noises during the sampling, we also derive the correlation function of the output noise for the proposed ideal C/D conversion.