This paper proposes a new receive scheme and a class of time domain second order polynomial Nyquist window functions, and applies them to Orthogonal Frequency-Division Multiplexing( OFDM) systems in order to reduce Inter-Carrier Interference (ICI) induced by frequency offset. This paper also analyzes the Signal to ICI plus Noise Ratio (SINR)and Bit Error Rate (BER) performances of the receiver. Additionally, this paper proposes a method to select optimum window parameters to maximize the SINR of the receiver thus providing an adaptive receiving capability. Our results show that the proposed method enables the use of unity roll-off factor, provides better SINR and BER than conventional receive methods whose roll-off factors are generally less than one. The new second order polynomial window is shown to provide better performance than raised cosine and "better than" Nyquist window.