Czaja, Wojciech Characterizations of Gabor systems via the Fourier transform. (English) Zbl 0966.42021 Collect. Math. 51, No. 2, 205-224 (2000). Consider a set of functions \(g^1,...,g^L \in L^2(R^d)\). Given nondegenerate \(d \times d\) matrices \(A,B\), the associated Gabor system is the set of functions \(\{e^{2\pi i Am \cdot x} g^k(x- Bn) \}_{m,n \in Z^d, k=1,..,L}\). The paper gives (in terms of the Fourier transform) equivalent conditions for the Gabor system to be an orthogonal system in \(L^2(R^d)\) or a tight frame. Reviewer: Ole Christensen (Lyngby) Cited in 9 Documents MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems Keywords:Gabor frame; tight frame; orthonormal basis PDFBibTeX XMLCite \textit{W. Czaja}, Collect. Math. 51, No. 2, 205--224 (2000; Zbl 0966.42021) Full Text: EuDML