Quantitative Assessment of Dual window Efficiency in Gabor Frame Expansions

Abstract: We investigate the performance of Gabor frame reconstructions using three compactly supported window functions: the second-order B-spline ($B_2$), the third-order B-spline ($B_3$), and the exponential B-spline of order 3 ($\varepsilon_3$). For each generator, various dual windows are considered, including the canonical dual, symmetric and asymmetric duals, and perturbation-based duals constructed via a recent duality result. The reconstruction quality is assessed using the Average Mean Squared Error (AMSE) across five standard test signals: Blocks, Bumps, Heavisine, Doppler, and Quadchirp. Numerical experiments demonstrate that exponential B-splines yield the lowest AMSE among the three, confirming their effectiveness in Gabor frame applications. Among the dual windows, the symmetric dual and its perturbation-based variant consistently achieve the best reconstruction accuracy, making them strong candidates for practical use in signal processing tasks.