ABSTRACT
A transformation in mathematics can broadly be defined as the operation which takes its input and "represents" it in a different form. Such a definition immediately implies preserving the essential characteristics of the input through several conservation rules or laws. In order to outline the complete input–output relationship in an abstract transformation, the input and output of the transformation should be characterized as well. Therefore, mathematically speaking, a transformation can be viewed as a special function whose input and output can be a single value or another function. Depending both on the transform and the input signal characteristics, different types of transforms exist in the literature. For instance, there are transforms which assume a deterministic input, whereas there are transforms operating on a stochastic input. A different way of classifying transforms is to consider the nature of the input signal such as continuous and discrete transforms, which assume continuous and discrete signals as input, respectively.
