Results from previous measurements on a small laboratory swirl burner undergoing self-excited acoustic oscillations with premixtures of either CH4 or C3H8 are summarized. The measurements of acoustic pressure and the distribution of chemiluminescent emission were used to deduce semi-empirical descriptions of the flame response functions, and these are used here in conjunction with a validated model for the acoustics of the premixture supply system, burner, and combustion chamber to reproduce the excitation frequencies and to deduce the required amplitudes of the flame response function. Variations of the burner flow rate and the equivalence ratio are examined, as is the sensitivity of the results to the acoustic and flame parameters. The results are of considerable relevance to the response of industrial gas-turbine combustion systems, and the calculations lay the foundations for the fundamental model of the flame response that is derived in Part II.