Alternating TR steady-state free precession (ATR SSFP) has been proposed as a method to achieve a favorable frequency response compared to that of conventional balanced SSFP. ATR SSFP, much like conventional SSFP, exhibits oscillatory transient signal behavior that can degrade image quality. Thus an efficient preparation scheme is desired in order to actively reduce this initial signal fluctuation. Using an approach similar to that of Le Roux [Simplified model and stabilization of SSFP sequences, J. Magn. Resonan. 163 (1) (2003) 23-37], we construct a mathematical model for ATR SSFP sequences and show a Fourier relation between the separated odd and even terms of the RF flip angle increment sequence during an initial preparation, and the resulting oscillatory residues. A weighted Kaiser-Bessel windowed ramp can be used to design preparation schemes for arbitrary TR(1), TR(2), and RF phase cycling combinations. Optimized Kaiser-Bessel windowed ramp preparations for wideband SSFP and fat-suppressed ATR SSFP imaging are tested in phantoms. The results show substantially reduced transient signal oscillation with this new initial preparation method.