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Wideband electromagnetic response can be extrapolated using combined low frequency and early time information, which can substantially reduce the computational load. Most existing extrapolation methods are based on orthogonal polynomials, but selecting optimal parameters of orthogonal polynomials is not straightforward. This work proposes to extrapolate wideband electromagnetic response using sparse representation. The electromagnetic response is expressed as linear combination of atoms from an overcomplete dictionary. Optimal linear combination of atoms is then sought through the affine scaling transformation and the support vector regression. By increasing the data length step by step, convergence of the sparse solution is used as a criterion to determine the sufficient data length. Performance analysis shows that our proposed extrapolation method retains lower computational complexity and renders more flexibility in reconstructing a signal. Numerical examples are presented to show the efficacy and advantages of the proposed extrapolation method.