How can I design a circuit that will generate a sinc function?
make two log amps, into one put a ramp signal, into the other put a sine wave. then the two signals go through an analog subtractor circuit, then an anti-log amp and voila -- sinc pulse. But it does have it's limitations and the inputs are of necessity pretty low. 

easiest way is still the lookup table, that is the way it's done even on medical equipment like magnetic resonance machines.