This paper introduces a novel filtering approach that employs integrated periodic structures with a conventional Vivaldi antenna to achieve a fully integrated bandpass filtering antenna. The approach results in a wide out-of-band suppression, high passband selectivity, adjustable operational bandwidth, and low insertion loss. The proposed filtering approach maintains the original size of the conventional Vivaldi antenna (base antenna) without requiring additional modifications. To validate the approach, we present two filtering Vivaldi antennas: filtering antenna I (center frequency: 18GHz, fractional bandwidth: 21%, insertion loss: 0.32dB) and filtering antenna II (center frequency: 6.5GHz, fractional bandwidth: 12%, insertion loss: 0.6dB). Their wide out-of-band gain suppression (typically ≥15dB) covers the conventional Vivaldi antenna's frequency range (4-24GHz). A prototype of the filtering antenna I is manufactured. Its measurement results validate the proposed approach and show good agreement with the simulated reflection coefficient, realized gain, and radiation patterns. The features of the proposed filtering antenna approach, make it suitable for various applications requiring efficient frequency filtering.INDEX TERMS Filtering antenna, fully integrated antenna design, metasurface, out-of-band suppression, wideband antenna, filtenna.