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In this paper, the filter-and-forward (FF) relay design for OFDM communication systems is considered to enhance the system performance over the conventional amplify-and-forward (AF) relaying scheme. The considered design criterion in this paper is to maximize the worst subcarrier channel signal-to-noise ratio (SNR) subject to the total relay transmit power constraint in order to improve the overall transmission quality-of-service. It is shown, by exploiting the eigen-property of circulant matrices and the structure of Toeplitz matrices, that the considered problem reduces to a semi-definite programming (SDP) problem. Numerical results are provided to validate our design method and the numerical results show that the proposed FF relay outperforms the AF scheme significantly.