The use of inhomogeneous but spatially correlated static and radiofrequency (RF) magnetic fields offers a potential methodology for performing magnetic resonance spectroscopy of samples placed outside the bore of the magnet. However, its practical implementation still presents challenging problems, among them the control of nuclear spins over broad frequency offset intervals. The present study introduces an efficient method of encoding the phase of the magnetization when the variation of the static field along the sample is much larger than the RF amplitude. The procedure is based on the use of consecutively applied full-passage adiabatic pulses. The induced phase modulation is broadband and selective because it does not depend on the offset relative to the central frequency and the limits can be sharply defined. Finally, the encoded phase depends almost linearly on the local RF amplitude. All these features enable the recovery of an inhomogeneity-free spectrum with amplitudes close to the theoretically attainable maximum.