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

For real bandlimited periodic signals, the author of proposed reconstruction formulas such that the ideal discrete-to-continuous-time (D/C) conversion can be realized within one period of the signal. However, for general complex bandlimited periodic signals, the results of 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.