Uncertainty principles and signal recovery. (English) Zbl 0689.42001

Summary: The uncertainty principle can easily be generalized to cases where the “sets of concentration” are not intervals. Such generalizations are presented for continuous and discrete-time functions, and for several measures of “concentration” (e.g., \(L_ 2\) and \(L_ 1\) measures). The generalizations explain interesting phenomena in signal recovery problems where there is an interplay of missing data, sparsity, and bandlimiting.


42A05 Trigonometric polynomials, inequalities, extremal problems
94A11 Application of orthogonal and other special functions
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