  We give a new and independent parameterization of the set of discrete series
characters of an affine Hecke algebra $\mathcal{H}_{\mathbf{v}}$, in terms of a
canonically defined basis $\mathcal{B}_{gm}$ of a certain lattice of virtual
elliptic characters of the underlying (extended) affine Weyl group. This
classification applies to all semisimple affine Hecke algebras $\mathcal{H}$,
and to all $\mathbf{v}\in\mathcal{Q}$, where $\mathcal{Q}$ denotes the vector
group of positive real (possibly unequal) Hecke parameters for $\mathcal{H}$.
By analytic Dirac induction we define for each $b\in \mathcal{B}_{gm}$ a
continuous (in the sense of [OS2]) family
$\mathcal{Q}^{reg}_b:=\mathcal{Q}_b\backslash\mathcal{Q}_b^{sing}\ni\mathbf{v}\to\operatorname{Ind}_{D}(b;\mathbf{v})$,
such that $\epsilon(b;\mathbf{v})\operatorname{Ind}_{D}(b;\mathbf{v})$ (for
some $\epsilon(b;\mathbf{v})\in\{\pm 1\}$) is an irreducible discrete series
character of $\mathcal{H}_{\mathbf{v}}$. Here
$\mathcal{Q}^{sing}_b\subset\mathcal{Q}$ is a finite union of hyperplanes in
$\mathcal{Q}$.
  In the non-simply laced cases we show that the families of virtual discrete
series characters $\operatorname{Ind}_{D}(b;\mathbf{v})$ are piecewise rational
in the parameters $\mathbf{v}$. Remarkably, the formal degree of
$\operatorname{Ind}_{D}(b;\mathbf{v})$ in such piecewise rational family turns
out to be rational. This implies that for each $b\in \mathcal{B}_{gm}$ there
exists a universal rational constant $d_b$ determining the formal degree in the
family of discrete series characters
$\epsilon(b;\mathbf{v})\operatorname{Ind}_{D}(b;\mathbf{v})$. We will compute
the canonical constants $d_b$, and the signs $\epsilon(b;\mathbf{v})$. For
certain geometric parameters we will provide the comparison with the
Kazhdan-Lusztig-Langlands classification.
