I would like a pair of complementary IIR filters (lowpass/highpass). By complementary, I mean, when the output from the two filters is summed, the original signal is recovered. I thought I could build such pairs with butterworth filters but using a little math, I discovered only 1st order filters were complementary. I thought I'd done this before, but I'm forgetting how.
Is something wrong with my math? Is there an easy solution I'm forgetting about?