Modal properties of a structure can be identified by experimental modal analysis (EMA). Discrete frequency response functions (FRFs) and impulse response functions (IRFs) between response and excitation series are bases for EMA. In the calculation of a discrete FRF, the discrete Fourier transform (DFT) is applied to both response and excitation series, and a transformed series in the DFT is virtually extended to have an infinite length and be periodic with a period equal to the length of the series; the resulting periodicity can be physically incorrect in some cases, which depends on an excitation technique used. An efficient and accurate methodology for calculating discrete FRFs and IRFs is proposed here, by which fewer spectral lines are needed and accuracies of resulting FRFs and IRFs can be maintained. The relationship between an IRF from the proposed methodology and that from the least-squares (LS) method is shown. A coherence function extended from a new type of coherence functions is used to evaluate qualities of FRFs and IRFs from the proposed methodology in the frequency domain. The extended coherence function can yield meaningful values even with response and excitation series of one sampling period. Based on the extended coherence function, a fitting index is used to evaluate overall qualities of the FRFs and IRFs. The proposed methodology was numerically and experimentally applied to a two degrees-of-freedom (2DOF) mass–spring–damper system and an aluminum plate to estimate their FRFs and IRFs, respectively. In the numerical example, FRFs and IRFs from the proposed methodology agree well with theoretical ones. In the experimental example, an FRF and its associated IRF from the proposed methodology with a random impact series agreed well with benchmark ones from a single impact test.