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In this paper, the optimal detection of an improper-complex second-order cyclostationary (SOCS) random signal is considered in the presence of an additive white Gaussian noise. To efficiently utilize the periodic and the symmetric spectral correlations in the signal, a linear-conjugate linear time-varying operator called properizing FREquency SHift (p-FRESH) vectorizer is employed, which converts the SOCS random process into an equivalent vector wide-sense stationary random process. The optimal likelihood ratio test is then derived in the time domain in the form of an estimator-correlator. A near-optimal practical detector structure is also proposed, which over-samples the observation in the time domain and block-processes it in the frequency domain in order to approximate the optimal detector. Numerical results show that the proposed detector significantly improves the detection performance by exploiting both the cyclostationarity and the impropriety of the improper-complex SOCS random signal.