Uncertainty principles as embeddings of modulation spaces

A class of new uncertainty principles is derived in the form of embeddings of Fourier– Lebesgue spaces into modulation spaces. These embeddings provide practical, sufficient conditions for a function to belong to a modulation space. Counterexamples based on the properties of Gabor expansions demonstrate that the embeddings are optimal.  2002 Elsevier Science (USA). All rights reserved.