The theoretical diffusion of ideal sorbate molecules along one-dimensional channels containing random sequences of high-energy and low-energy barriers has been studied. This situation might occur in the case of sorbate diffusion in one-dimensional zeolite channels containing two cationic species of different diameters attached to the aluminosilicate framework. Using a master equation with appropriate microscopic transfer rates characterising the transfer of sorbate molecules between neighbouring cells, the frequency response of the number of absorbed molecules to a periodic modulation of the sorbate concentration at the entrances to the channels has been calculated. For channels consisting of about 100 equal-height energy barriers the frequency response function agrees well with the continuum result obtained from the Fickian diffusion equation. Predictions for the frequency response functions when fast and slow microscopic transfer rates operate in each channel have been made. The presence of two distinct transfer rates gives rise to well-resolved low- and high-frequency features. The relevance of these results to experiments on porous materials is discussed.