This paper deals with the statistical analysis of the behavior of a blind copyright protection watermarking system based on pseudorandom signals embedded in the magnitude of the Fourier transform of the host data. The host data that the watermark is embedded into is one-dimensional and nonwhite, following a specific model. The analysis performed involves theoretical evaluation of the statistics of the Fourier coefficients and an optimum detector design for multiplicative embedding. It is proved that the widely used correlator is not the optimum detector. Finally, experimental results are presented in order to show the proposed detector's efficiency versus that of the correlator detector.