2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142224We consider signals and operators in finite dimension which have sparse time-frequency representations. As main result we show that an $S$-sparse Gabor representation in $\mathbb{C}^n$ with respect to a random unimodular window can be recovered by Basis Pursuit with high probability provided that $S\leq Cn/\log(n)$. Our results are applicable to the channel estimation problem in wireless communications and they establish the usefulness of a class of measurement matrices for compressive sensing.Classical Analysis and ODEsInformation Theory42C40; 15A52; 90C25text