A.J.E.M. Janssen
Classroom Proof of the Density Theorem for Gabor Systems
Preprint series: ESI preprints

MSC:

42C15 Series of general orthogonal functions, generalized Fourier expansions, nonorthogonal expansions

94A05 Communication theory, See also {60G35, 90B12}

94A12 Signal theory (characterization, reconstruction, etc.)

Abstract: In this note we present a short and easy proof of the density theorem for Gabor
systems $(g,a,b)$:
(i) when $(g,a,b)$ is a Gabor frame we have $ab\leq1$,
(ii) when $(g,a,b)$ is a Riesz-Gabor basis we have $ab\geq1$.



Keywords: Gabor frame, Riesz-Gabor basis, density, duality principle, Gabor representation, OFDM