pseudorandom number generators (see [@Nie92a]), the well known $(n\alpha)_{n\ge 0}$ sequences (see [@Kui74a]), or the block cipher AES in Output Feedback mode (see [@Daemen02a p. 28]).

In some other cases, we employ a ring $(R,+, \cdot)$ with unity $1$ and a function $\psi: R\rightarrow {\ensuremath{\mathcal{S}}}$ to map the sequence $(n1)_{n\ge 0}$ (the so-called “counter”) first to a sequence of states $(\psi(n1))_{n\ge 0}$ in ${\ensuremath{\mathcal{S}}}$. Then, this sequence is “encrypted” by $T$ to give the sequence $(T\circ\psi(n1))_{n\ge 0}$ in ${\ensuremath{\mathcal{S}}}$. Finally, this sequence of states is mapped into the output space ${\ensuremath{\mathcal{O}}}$. This gives $\omega=(\varphi\circ T\circ\psi(n1))_{n\ge 0}$. Examples of such constructions are explicit inversive congruential pseudorandom number generators (see [@Hel95c; @Nie10b; @Nie11a; @Topuzoglu07a]), certain digital sequences (see [@Dick10a]), or AES in Counter mode (see [@Daemen02a p. 28]). In these examples, we let $R={\ensuremath{\mathbb{Z}}}$, the integral domain of integers.

In all of the cases exhibited above, we employ some arithmetical operation like addition on the state space ${\ensuremath{\mathcal{S}}}$. If ${\ensuremath{\mathcal{S}}}$ is a compact abelian group with respect to the chosen operation, then we have the arsenal of abstract harmonic analysis at our disposition (see [@Hewitt79a]). The choice of the compact group ${\ensuremath{\mathcal{S}}}$ determines which function system is suitable for the analysis of 