  We study a recently introduced base $b$ polynomial analog of Stern's diatomic
sequence, which generalizes Stern polynomials of Klavar, Dilcher, Ericksen,
Mansour, Stolarsky, and others. We lift some basic properties of base $2$ Stern
polynomials to arbitrary base, and introduce a matrix characterization of Stern
polynomials. By specializing, we recover some new number theoretic results
about hyper $b$-ary partitions, which count partitions of $n$ into powers of
$b$.
