Digital watermarking of audio, image, video or multimedia data is achieved by inserting the watermark into the perceptually significant components of a decomposition of the data in a manner so as to be visually imperceptible. In a preferred method, a frequency spectral image of the data, preferably a Fourier transform of the data, is obtained. A watermark is inserted into perceptually significant components of the frequency spectral image. The resultant watermarked spectral image is subjected to an inverse transform to produce watermarked data. The watermark is extracted from watermarked data by first comparing the watermarked data with the original data to obtain an extracted watermark. Then, the original watermark, original data and the extracted watermark are compared to generate a watermark which is analyzed for authenticity of the watermark.