On Quadrature Sampling of Bandpass Signals

Deterministic bandpass signals are considered in which the nonzero portions of the signal spectrum are confined to the frequency region 0⩽ ω0 - σ/2 ⩽ |ω| ⩽ω0 + σ/2, where σ > 0 is the "bandwidth" of the signal. Quadrature sampling, as introduced by O. D. Grace and S. P. Pitt, requires uniform sampling of both the bandpass signal and its quarter wavelength (based on nominal frequency ω0) translation, each at a common sampling rate depending on the exact relationship between ω0 and σ. When th intersample sample spacing is properly chosen, the bandpass signal can be reconstructed in its entirety from knowledge of the sample values; moreover, with quadrature sampling, the (low-pass) in-phase and quadrature components of the bandpass signal have a simple explicit representation in terms of samples of the original bandpass signal. Time domain techniques, in particular the theory of orthogonal expansions, are here used to derive the quadrature sampling theorem as well as the uniform sampling theorem for bandpass signals, a result usually derived from frequency (spectral) considerations. The resulting minimum sampling rate for the quadrature sampling theorem provides a reduction in the sampling rate previously announced by Grace and Pitt.