The existence of cepstra for two-dimensional rational polynomials

The use of cepstral analysis is helpful for some problems where two one-dimensional signals are combined by convolution [1]. In such problems it is important to ensure that the phase function associated with the resultant signal may be defined so that it is a continuous, odd, and periodic function of frequency [2], [3]. One class of one-dimensional signals which have this property is the class whose z-transforms are rational polynomials [2]. In this correspondence, we shall show that these results are extendible to two dimensions, and that 2-D cepstra can be defined for 2-D rational polynomials.