For studying atmospheric phenomena and monitoring climate change, radar has been proven to be an indispensable and dependable tool. A Doppler radar also allows for the observation of particle velocities and filtering of the received signal in the frequency domain. A polarimetric radar exploits the anisotropy of the precipitation medium by employing pulses of different polarizations. A Doppler polarimetric radar not only combines both aforementioned advantages, but also offers the possibility to interpret the radar observables as functions of the particle velocities instead of single, integrated values. This option of finely partitioning the radar resolution volume results in abounding information which seems attractive; however, careful consideration should be placed on how to process it in order to access its content and avoid pitfalls. This paper presents rain measurements carried out by the IDRA X-band Doppler polarimetric radar located in Cabauw, the Netherlands. The focus is on the estimation of differential phase (¿dp) and specific differential phase (Kdp), from a spectral polarimetric point of view. With an adequate spectral polarimetric processing, it is expected to improve the estimates of ¿dp and Kdp. Comparison with the established, time-domain technique will be carried out. Kdp is challenging to estimate because it is a phase-related observable and the phase of radar signal presents rapid variations, necessitating careful processing and filtering. Yet, it is valuable, as it has been sufficiently supported in literature that it results in advantageous rain rate retrieval and classification algorithms.@en