  In this paper we discuss the motivation, design, and analysis of ambisonic
decoders for systems where the vertical order is less than the horizontal
order, known as mixed-order Ambisonic systems. This can be due to the use of
microphone arrays that emphasize horizontal spatial resolution or speaker
arrays that provide sparser coverage vertically. First, we review Ambisonic
reproduction criteria, as defined by Gerzon, and summarize recent results on
the relative perceptual importance of the various criteria. Then we show that
using full-order decoders with mixed-order program material results in poorer
performance than with a properly designed mixed-order decoder. We then
introduce a new implementation of a decoder optimizer that draws upon
techniques from machine learning for quick and robust convergence, discuss the
construction of the objective function, and apply it to the problem of
designing two-band decoders for mixed-order signal sets and non-uniform
loudspeaker layouts. Results of informal listening tests are summarized and
future directions discussed.
