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We give a new and independent parameterization of the set of discrete seriescharacters of an affine Hecke algebra $\mathcal{H}_{\mathbf{v}}$, in terms of acanonically defined basis $\mathcal{B}_{gm}$ of a certain lattice of virtualelliptic characters of the underlying (extended) affine Weyl group. Thisclassification applies to all semisimple affine Hecke algebras $\mathcal{H}$,and to all $\mathbf{v}\in\mathcal{Q}$, where $\mathcal{Q}$ denotes the vectorgroup of positive real (possibly unequal) Hecke parameters for $\mathcal{H}$.By analytic Dirac induction we define for each $b\in \mathcal{B}_{gm}$ acontinuous (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 $\epsilon(b;\mathbf{v})\operatorname{Ind}_{D}(b;\mathbf{v})$ (forsome $\epsilon(b;\mathbf{v})\in\{\pm 1\}$) is an irreducible discrete seriescharacter 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 discreteseries characters $\operatorname{Ind}_{D}(b;\mathbf{v})$ are piecewise rationalin the parameters $\mathbf{v}$. Remarkably, the formal degree of$\operatorname{Ind}_{D}(b;\mathbf{v})$ in such piecewise rational family turnsout to be rational. This implies that for each $b\in \mathcal{B}_{gm}$ thereexists a universal rational constant $d_b$ determining the formal degree in thefamily of discrete series characters$\epsilon(b;\mathbf{v})\operatorname{Ind}_{D}(b;\mathbf{v})$. We will computethe canonical constants $d_b$, and the signs $\epsilon(b;\mathbf{v})$. Forcertain geometric parameters we will provide the comparison with theKazhdan-Lusztig-Langlands classification.

A uniform classification of discrete series representations of affine Hecke algebras