Accurate complex-permittivity data are essential for electromagnetic simulation and device design in plasmonics, nanophotonics, infrared optics, and terahertz technologies. The complex permittivity, ε(ω) = ε'(ω) + iε''(ω), determines the intrinsic electromagnetic response of metallic materials, including reflection, absorption, scattering, surface-plasmon excitation, propagation loss, and field penetration. However, reported optical constants of metals often exhibit significant discrepancies. These discrepancies arise from differences in sample preparation, film thickness, surface roughness, measurement methods, and spectral ranges. Moreover, many available datasets are limited to narrow wavelength intervals, which makes it diffcult to obtain continuous and reliable permittivity curves over a broad spectral range. Conventional parametric models, such as the Drude, Lorentz-Drude, and Brendel-Bormann models, can describe free-electron and interband-transition responses. Nevertheless, their accuracy strongly depends on the assumed oscillator form, fitting range, and optimized parameters. Their applicability to broadband and cross-band simulations is therefore limited. To address these issues, a data-driven non-parametric reconstruction method is proposed in this work to obtain continuous, smooth, and physically consistent complex-permittivity curves for Au, Ag, Cu, and Al from the extreme ultraviolet to the terahertz regime. Publicly available experimental optical-constant datasets are first integrated. Reliable spectral segments are then selected according to spectral coverage, overlap, traceability, physical consistency, minimal complex-permittivity deviation, and derivative continuity. Since the original data are highly nonuniformly distributed over several orders of magnitude in wavelength, the wavelength variable is transformed onto a logarithmic scale. Natural cubic-spline interpolation and equidistant resampling are subsequently performed along the logarithmic wavelength axis. In this way, uniformly sampled data suitable for signal reconstruction are generated. Based on the Nyquist sampling theorem, a local sinc reconstruction formula is introduced to recover continuous dielectric spectra from the resampled data. To suppress truncationinduced oscillations and high-frequency noise, the sinc kernel is localized using a Kaiser window. The reconstructed sequence is further smoothed using a Savitzky-Golay filter. The window length and shape parameter are optimized through reconstruction-error analysis, so that the main dispersion features are retained while numerical artifacts are reduced. The reconstructed permittivity curves of Au, Ag, Cu, and Al exhibit continuous and smooth wavelength-dependent behavior across the ultraviolet, visible, infrared, and terahertz regions. Compared with representative Rakić-LD, Rakić-BB, and Werner-DFT reference models, the proposed sinc-based method achieves lower errors in both the real and imaginary parts of the dielectric function. This improvement is particularly evident near spectral boundaries, where conventional models often show noticeable deviations. Kramers-Kronig consistency analysis further confirms that the reconstructed spectra preserve physical self-consistency within the effective experimental bandwidth. To evaluate the practical value of the reconstructed model, the obtained permittivity data are applied to localized surface plasmon resonance simulations of metallic nanoparticles, surface plasmon polariton propagation-length calculations, and metallic skin-depth analysis. The results indicate that the proposed model predicts the LSPR resonance wavelength and spectral line shape more accurately than traditional parametric models. The calculated SPP propagation length and metal skin depth also agree well with reported experimental and literature data. These results demonstrate that the combination of logarithmic-wavelength resampling, local sinc reconstruction, Kaiser windowing, and Savitzky-Golay filtering provides a data-driven, non-parametric, and reproducible route for broadband complex-permittivity reconstruction. Dependence on predefined physical fitting models is reduced, while the measured dispersion characteristics of metals are preserved. The reconstructed permittivity curves provide accurate and continuous material parameters for plasmonic, nanophotonic, infrared, and terahertz device simulations. They also offer a practical route from material-data reconstruction to device-performance prediction in broadband electromagnetic design.