  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.
