A frequency domain (FD) time-reversal (TR) pre-coder is proposed to perform physical layer security (PLS) in single-input single-output (SISO) system using orthogonal frequency-division multiplexing (OFDM). To maximize the secrecy of the communication, the design of an artificial noise (AN) signal well-suited to the proposed FD TR-based OFDM SISO system is derived. This new scheme guarantees the secrecy of a communication toward a legitimate user when the channel state information (CSI) of a potential eavesdropper is not known. In particular, we derive an AN signal that does not corrupt the data transmission to the legitimate receiver but degrades the decoding performance of the eavesdropper. A closed-form approximation of the AN energy to inject is defined in order to maximize the secrecy rate (SR) of the communication. Simulation results are presented to demonstrate the security performance of the proposed secure FD TR SISO OFDM system.