CalculationsoftheElectroMagnetic(EM)responseproducedbyalargehorizontalloopplacedoverlayeredmediumarerathercomplexbecauseitsintegralexpressioncontainstheproductoftwoBesselfunctionsandhasapergentterm.Inthispaper,animprovedfastHankelandGaver-Stehfesttransformsareintroducedtosolvethestrong-oscillationandslow-decaypropertiesoftheintegrand,whereoneBesselfunctionintheproductissubstitutedbyacarefullychosenpolynomialofhighaccuracyandtheotherusedasthedigitalfiltercoefficientsintheconvolutionintegral.Comparisonsprovethevalidityandtheefficiencyoftheproposedmethod.