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Description
The well known direct signal control (DSC) approach allows us to optimize excitation voltages of a MRI pulse sequence in such a way that the overall transverse magnetization of a spin ensemble has desired values at a number of signal readout times. In this approach the overall transverse magnetization is calculated with the help of an approximate solution of the Bloch equations and corresponding transformations of a finite number of Fourier coefficients through the pulse sequence. We develop an equivalent alternative calculation method without Fourier coefficients. This formulation uses a finite number of discrete spins and the approximate solution of the Bloch eqquations for these spins. We show that the relevant Fourier coefficients of DSC can be obtained from a discrete Fourier transfom of the magnetizations of these spins. We specify how to select the positions and initial magnetizations of the discrete spins to get identical overall magnetizatios at the readout times as with DSC.