Figure 1

Filter construction. Visualization of the available control space for an \(n=8\) segment control sequence. The filter is synthesized over the parameters presented in \(\boldsymbol {\Gamma }_{n}\), whose transpose corresponds to the discrete time segments in the time-domain filter. As an illustration, a time-varying Rabi rate (arbitrary units) is presented for each of the l segments. Synthesis of this waveform may be constructed in the Walsh basis using the Hadamard transform (notation upper right), as will be discussed in Section 5.