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In this paper we present a construction of frames generated by a single band-limited function for decomposition smoothness spaces on $$\mathbb R ^d$$ R d of modulation and Triebel–Lizorkin type. A perturbation argument is then used to construct compactly supported frame generators.
We construct an orthonormal basis for the family of bi-variate α-modulation spaces. The construction is based on local trigonometric bases, and the basis elements are closely related to so-called brushlets. As an application, we show thatm-term nonlinear approximation with the representing system in an α-modulation space can be completely characterized.
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