Local uncertainty principles for the Cohen class. (English) Zbl 1336.42007
Summary: In this paper we analyze time-frequency representations in the Cohen class, i.e., quadratic forms expressed as a convolution between the classical Wigner transform and a kernel, with respect to uncertainty principles of local type. More precisely, the results we obtain concerning the energy distribution of these representations show that a “too large” amount of energy cannot be concentrated in a “too small” set of the time-frequency plane. In particular, for a signal \(f\in L^2(\mathbb R^d)\), the energy of a time-frequency representation contained in a measurable set \(M\) must be controlled by the standard deviations of \(|f|^2\) and \(|\hat f|^2\), and by suitable quantities measuring the size of \(M\).
MSC:
| 42B08 | Summability in several variables |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
Keywords:
time-frequency representations; Wigner sesquilinear and quadratic form; local uncertainty principlesReferences:
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