Two-Dimensional Partially Differential Cepstrum and Its Applications on Filter Stabilization and Phase Unwrapping

A new type of differential cepstrum (DC) named as partially DC (PDC) is introduced. While compared with the previously defined DC, the PDC saves half the computational complexity since only one dimension of the partial derivative is considered. Nevertheless, for the calculation of the complex cepstrum (CC), using the PDC avoids the phase-unwrapping routine as well. One application is to construct the minimum-phase sequence from a mixed-phase one through a windowing technique, which can be further applied to filter stabilization. Another application is performing phase unwrapping on 2-D phase data to which we propose a much simpler technique using the PDC. These applications can be implemented in a more efficient and convenient way with the PDC than with the traditional DC.