We propose a spectrum regeneration and demodulation method for multiple direct RF undersampled real signals by using a new algorithm. Many methods have been proposed to regenerate the RF spectrum by using undersampling because of its simple circuit architecture. However, it is difficult to regenerate the spectrum from a real signal that has a band wider than a half of the sampling frequency, because it is difficult to include complex conjugate relation of the folded spectrum into the linear algebraic equation in this case. We propose a new spectrum regeneration method from direct undersampled real signals that uses multiple clocks and an extended algorithm considering the complex conjugate relation. Simulations are used to verify the potential of this method. The validity of the proposed method is verified by using the simulation data and the measured data. We also apply this algorithm to the demodulation system.

This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.