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A nonuniform fast Fourier transform (NUFFT) technique is incorporated into the spectral-domain approach for the analysis of shielded single and multiple coupled microstrip lines. Each of the spectral-domain Green's functions is decomposed into an asymptotic part and a remaining part. At the interface of layered dielectrics with conducting strips, the product of a basis function and an associated Green's function constitutes an expansion E-field. The inverse Fourier transform (IFT) of the expansion E-field is its spatial distribution all over the interface. We take this advantage to match the final boundary conditions on all the conducting strips simultaneously. As a result, if all the strips are at one interface, the number of operations required in this method is proportional to Nℓ, but not to Nℓ2, where Nℓ is the number of the strips. The IFT of the asymptotic part of each expansion E-field can be obtained analytically, and that of the remaining part can be quickly processed by the NUFFT. The Gauss-Chebyshev quadrature is used to accelerate the computations of the integrals resulted from the Galerkin's procedure. The proposed method is also applied to investigate the dispersion characteristics of coupled lines with finite metallization thickness and of coupled lines at different levels. A convergence analysis of the results is presented and a comparison of used CPU time is discussed.