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Frequency-invariant (FI) beamforming for wideband antenna arrays inevitably involves array aperture loss at the higher-end frequencies of the bandwidth. In order to minimize aperture loss and to fully utilize the array aperture at different operation frequencies, an optimal wideband beamformer for uniform linear array (ULA) is designed based on Dolph-Chebyshev's theory of beamforming. Different from the existing FI beamformers for wideband arrays, our wideband beamformer produces frequency-dependent patterns which have the narrowest mainlobe width for any given equiripple sidelobe level over a wide frequency bandwidth. These frequency-dependent patterns are obtained through using the system identification method to determine the transfer function of the beamforming network. A matrix formulation is developed to calculate the frequency-dependent optimal Riblet-Chebyshev weights for element spacings smaller than half wavelength. The transfer function of the beamforming network, which is treated as an equivalent multi-input and single-output (MISO) system, is then obtained by the method of system identification with the optimal frequency-dependent Riblet-Chebyshev weights as the input data. Numerical results are provided to verify the effectiveness and validity of the proposed method.