We propose a generalized Shinnar-Le-Roux transform that maps $$$T_1$$$, $$$T_2$$$ and frequency selective pulses to multi-dimensional polynomials. We show that the polynomial mapping is one-to-one and hence designing these RF pulses reduces to multi-dimensional polynomial design. We describe a convex approach to the multi-dimensional polynomial design and show preliminary $$$T_2$$$ and frequency selective pulses.
