integer base $\mathbf b=(b_1, \ldots, b_s)$ on the $s$-torus $[0,1)^s$, is generated by [*addition with carry*]{} of digit vectors. For this reason, it makes sense to choose as the underlying group ${\ensuremath{\mathcal{S}}}$ the compact group of $\mathbf b$-adic integers ${\ensuremath{\mathbb{Z}}}_{b_1}\times\dots\times{\ensuremath{\mathbb{Z}}}_{b_s}$. Considering the dual group then leads to the ${\ensuremath{\mathbf b}}$-adic function system, which is the main tool of the ${\ensuremath{\mathbf b}}$-adic method introduced in [@Hel09a; @Hel10a; @Hel10c]. It will be discussed in Section \[s:notation\].

The general duality principle presented before also accommodates for *hybrid sequences*, which are sequences $\omega$ of points in $[0,1)^s$ where certain coordinates of the points stem from one lower-dimensional sequence $\omega_1$, with state space ${\ensuremath{\mathcal{S}}}_1$, and the remaining coordinates from a second lower-dimensional sequence $\omega_2$, with state space ${\ensuremath{\mathcal{S}}}_2$. The duality principle leads us to consider *hybrid function systems*, which arise from the product group $\hat{{\ensuremath{\mathcal{S}}}}_1\times \hat{{\ensuremath{\mathcal{S}}}}_2$. Of course, this idea may be generalized to mixing more than two subsequences into a hybrid sequence.

This paper is structured as follows. In Section \[s:addition\] we consider the question which function systems will suffice to analyze digital sequences. In Section \[s:notation\] we introduce the necessary notation and in Section \[s:spectral\] we define the hybrid spectral test and show 