a technique has previously been described for generating optimal rf pulse sequences using finite impulse response filter techniques to calculate the fourier series which would yield the desired z and xy magnetizations in a magnetic resonance imaging device . such a technique is now extended to allow for control of the input pulse shape as well as the frequency response . since the peak power is limited by the amplifier power and the total energy of the pulse is limited by the specific absorption rate of the tissue or sample , it is desired to limit the peak power and total energy of the input pulse without degrading the resulting excitation . this is accomplished by recognizing that the total energy of the pulse is encoded in the lowest order fourier series coefficients of the frequency response and then specifying the total energy of the pulse as a design parameter to the rf pulse synthesis algorithm . peak power of the pulse may also be limited by selecting roots for β , where m z =. linevert split . α . linevert split . 2 -. linevert split . β 2 , which leads to pulses with variable phase yet do not change the overall frequency response . by appropriately selecting α and β , a hard pulse sequence is generated which serves as the basis for a shaped pulse which meets the desired constraints on the input pulse shape .