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This paper investigates frequency domain detection of a phase coded signal for unknown arrival time and amplitude in radar applications. The signal is barker coded pulse. A sub-optimal detector, i.e. generalized likelihood ratio test (GLRT) is used which replaces the unknown parameters by their maximum likelihood estimates and then pulse embedded in colored noise is detected. The main advantage of this scheme is that the case of colored noise can be handled. The spectral detector is evaluated through Monte Carlo (MC) simulations and receiver operating characteristic (ROC) is plotted for various signal-noise scenarios.