On the influence of microphone array geometry on the behavior of hypercomplex adaptive filters

The performance of hypercomplex adaptive filters has been widely experimented during the last decade. Quaternion filters, especially, have been utilized in systems where the signals to be processed have some form of correlation. However, besides correlation, some resolved explanation about what particular algebra to use in a certain context has not been provided, yet. This work tries to contribute in this direction by proposing an experiment that puts filters to the test with changing the input signal geometry. The tests presented in this paper take place in acoustic environment and show how a proper sound space transformation, along with the choice of the mathematical format for processing, can improve a filter performance.