Equi-ripple design of quadratic-phase RF pulses

An improved strategy for the design of quadratic-phase RF pulses with high selectivity and broad bandwidths using the Shinnar-Le Roux (SLR) transformation is proposed. Unlike previous implementations, the required quadratic-phase finite impulse response (FIR) filters are generated using the complex Remez exchange algorithm, which ensures an equi-ripple deviation from the ideal response function. It is argued analytically that quadratic-phase pulses are near-optimal in terms of minimising the B1-amplitude for a given bandwidth and flip angle. Furthermore, several parameter relations are derived, providing practical design guidelines. The effectiveness of the proposed design method is demonstrated by examples of excitation and saturation pulses applied in vitro and in vivo.