ABSTRACT

This chapter introduces the 2-D z transform and its inverse and discusses some of their properties. In the second half of the chapter, the 2-D Fourier transform and its inverse are introduced and some of their properties are discussed. The 2-D sampling theorem is then introduced as the fundamental link between 2-D continuous and discrete signals. The properties of the z transform can be described by means of a number of theorems that are straightforward extensions of their 1-D counterparts. By analogy, the z transform of a product of two space-domain functions can be formed by using the complex convolution. The 2-D Fourier transform is a straightforward extension of its 1-D counterpart and its importance in the study of 2-D digital filters arises from the fact that 2-D discrete signals are very frequently generated by sampling corresponding 2-D continuous signals. Digital filters and digital signal processing in general owe their widespread applications to the sampling theorem.