Extraction of In-Phase and Quadrature Components by Time-Encoding Sampling

Time encoding machine (TEM) is a biologically-inspired scheme to perform signal sampling using timing. In this paper, we study its application to the sampling of bandpass signals. We propose an integrate-and-fire TEM scheme by which the in-phase (I) and quadrature (Q) components are extracted through reconstruction. We design the TEM according to the signal bandwidth and amplitude instead of upper-edge frequency and amplitude as in the case of bandlimited/lowpass signals. We show that the I and Q components can be perfectly reconstructed from the TEM measurements if the minimum firing rate is equal to the Landau's rate of the signal. For the reconstruction of I and Q components, we develop an alternating projection onto convex sets (POCS) algorithm in which two POCS algorithms are alternately iterated. For the algorithm analysis, we define a solution space of vector-valued signals and prove that the proposed reconstruction algorithm converges to the correct unique solution in the noiseless case. The proposed TEM can operate regardless of the center frequencies of the bandpass signals. This is quite different from traditional bandpass sampling, where the center frequency should be carefully allocated for Landau's rate and its variations have the negative effect on the sampling performance. In addition, the proposed TEM achieves certain reconstructed signal-to-noise-plus-distortion ratios for small firing rates in thermal noise, which is unavoidably present and will be aliased to the Nyquist band in the traditional sampling such that high sampling rates are required. We demonstrate the reconstruction performance and substantiate our claims via simulation experiments.