A deterministic bandpass signalx(t) bandlimited to ‖ ω ‖ ε I1≡(ω0−σ/2, ω0+σ/2) can be represented in the formx(t)=p1(t) cosω0′t−q1(t) sinω0′t, wherep1,q1are low‐pass (the ’’in phase’’ and ’’quadrature’’) components bandlimited to ‖ ω ‖?σ/2+‖ ω0−ω0′ ‖ and ω0′ is an arbitrary frequency within the bandI1. Quadrature sampling has as its aim the recovery of the low‐pass componentsp1,q1directly from samples of both the bandpass signalx(t) and its quarter‐wavelength translationx(t−π/2ω0′), the samples being taken at a low‐pass rate. Grace and Pitt [J. Acoust. Soc. Am. 44, 1453 (1968)] obtained a result for the case ω0′=ω0?σ requiring an overall oraveragesampling rate of (σ/π)(γ/[γ]) samples/s, where γ=ω0/σ and [⋅] denotes the greatest integer function. By reducing the problem to an application of the classical Shannon sampling theorem in a special case (2ω0/σ =integer) and then proceeding to the general case via an embedding technique, we arrive here at an improved average sampling rate of (2γ+1/[2γ+1])(σ/π) samples/s. The method, assuming only ω0?σ/2 and finite energy signals, provides a simpler and more accessible treatment of the quadrature sampling problem than the earlier techniques of Grace and Pitt, Kohlenberg [J. Appl. Phys. 24, 1432 (1953)], and the author [IEEE Trans. Aerosp. Electron. Syst. AES‐15, 366 (1979)].