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The Dirac-{\delta} distribution may be realized through sequences ofconvlutions, the latter being also regarded as approximation to the identity.The present study proposes the so called pre-orthogonal adaptive Fourierdecomposition (POAFD) method to realize fast approximation to the identity. Thetype of sparse representation method has potential applications in signal andimage analysis, as well as in system identification.

Sparse Approximation to the Dirac-{\delta} Distribution