•In the spatial domain a combination between the data value samples provides reasonable SNR results (more than 66dB).•These approaches are simple and inexpensive in computation time can be used for real-time watermarking required in low-power environments.•The use of transforms makes the message more robust to compression, since it uses the same space used for coding.•The results obtained remain satisfactory compared to some recent work with a SNR greater than 33dB on average.•The decomposition into sub-bands provides acceptable and satisfactory levels of SNR compared to some recent work with a SNR greater than 40dB. In this paper; we propose two new substitution schemes for digital audio watermarking based on the Fourier transform. The integration of the watermark will be performed by combining the parity of the successive coefficients values; each variant will represent a different combination. In our experiments several variants of the Fourier transform are used (Discrete Fourier Transform, a Fractional Fourier Transform as well as a Quaternion Discrete Fourier Transform). For each transform, both variants of our watermarking scheme are applied and the results obtained show that our approach offers good imperceptibility and generates watermarked audio sample robust against various attacks with a high-quality watermark. However, using small audio file for our experiments considerably reduces the capacity of our approach in the frequency domain.