Digital watermarks have been proposed as a method for discouraging illicit copying and distribution of copyrighted material, and to create secure digital image libraries by adding to images copyright and user-right information. Using a robust digital watermark to detect and trace copyright violations has therefore lot of interest. This paper describes an approach to embedding a digital watermark using the Fourier transform. The paper also addresses the difficult problem of oblivious watermark detection. It is shown that, for the CDMA spread spectrum signal described in the paper, it is still possible to positively detect the presence of a watermark without being able to decode it (and even infer the number of bits contained in the watermark) given only the key used to generate it. Finally, through experimental results the usefulness of such measure is shown.