  This paper is concerned with the characterization of $\alpha$-modulation
spaces by Banach frames, i.e., stable and redundant non-orthogonal expansions,
constituted of functions obtained by a suitable combination of translation,
modulation and dilation of a mother atom. In particular, the parameter $\alpha
\in [0,1]$ governs the dependence of the dilation factor on the frequency. The
result is achieved by exploiting intrinsic properties of localization of such
frames. The well-known Gabor and wavelet frames arise as special cases ($\alpha
= 0$) and limiting case ($ \alpha \to 1)$, to characterize respectively
modulation and Besov spaces. This intermediate theory contributes to a further
answer to the theoretical need of a common interpretation and framework between
Gabor and wavelet theory and to the construction of new tools for applications
in time-frequency analysis, signal processing, and numerical analysis.
