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A new unified formulation for seven different orthogonal frequency-division multiplexing (OFDM) systems is presented. The proposed formulation relies on six parameters and encompasses conventional OFDM systems, with windowing in the transmitter and/or in the receiver, and also with a cyclic prefix (CP) or both a CP and cyclic suffix (CS). A new equivalent channel matrix that is useful for calculating both the received signal and the intersymbol and intercarrier interference power is defined and characterized. Unlike previous works, this new channel matrix formulates the channel convolution with no restrictions on the length of the channel impulse response. Moreover, it includes the overlap-and-add procedure performed in the transmitter of windowed OFDM systems. Furthermore, new theoretical expressions for the intersymbol and intercarrier interference and also for the signal-to-interference-plus-noise ratio are derived.