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The phase of an audio/speech signal conveys critical information, which is exploited in a variety of applications. Accurate phase information extraction is a prerequisite for applications such as coding, synchronization, synthesis or recognition. However, signal phase extraction is not a straightforward procedure, mainly due to the discontinuities appearing in it (phase 'wrapping' effect). In previously published work, the Hartley phase cepstrum was proposed in order to encapsulate the phase content of a signal efficiently as a viable alternative based on its properties and advantages compared to the Fourier phase cepstrum. In this work, the relationships among the time domain, the phase spectrum and the phase cepstrum for the Fourier case and for the Hartley case, are established. Moreover, the Hartley phase spectrum is further processed, aiming to represent the phase content of a signal accurately.