This thesis investigates the development of digital audio watermarking in addressing issues such as copyright protection. Over the past two decades, many digital watermarking algorithms have been developed, each with its own advantages and disadvantages. The main aim of this thesis was to develop a new watermarking algorithm within an existing Fast Fourier Transform framework. This resulted in the development of a Complex Spectrum Phase Evolution based watermarking algorithm. In this new implementation, the embedding positions were generated dynamically thereby rendering it more difficult for an attacker to remove, and watermark information was embedded by manipulation of the spectral components in the time domain thereby reducing any audible distortion. Further improvements were attained when the embedding criteria was based on bin location comparison instead of magnitude, thereby rendering it more robust against those attacks that interfere with the spectral magnitudes. However, it was discovered that this new audio watermarking algorithm has some disadvantages such as a relatively low capacity and a non-consistent robustness for different audio files. Therefore, a further aim of this thesis was to improve the algorithm from a different perspective. Improvements were investigated using an Singular Value Decomposition framework wherein a novel observation was discovered. Furthermore, a psychoacoustic model was incorporated to suppress any audible distortion. This resulted in a watermarking algorithm which achieved a higher capacity and a more consistent robustness. The overall result was that two new digital audio watermarking algorithms were developed which were complementary in their performance thereby opening more opportunities for further research.