ABSTRACT
The main purpose of this part is to establish the mathematical concepts, theorems, and results that are critical to our understanding of the various algorithms. As these results are developed, care is taken to cast them in a way that exposes their close connection to digital signal processing algorithms. In this regard, the contents of this section deal with the following topics:
Number systems that arise in digital signal processing systems and applications; these include infinite as well as finite number systems.
Polynomial extension fields and rings.
Number theoretic results pertaining to data sequences and their indices; these include the Chinese remainder theorem for integers.
Polynomial algebra over infinite and finite number systems; these include the Chinese remainder theorem for polynomials defined over fields (infinite and finite) and finite integer rings.
Concept of the primitive roots and their existence for different number systems.
Theoretical aspects of various convolution and DFT algorithms.
Cyclotomic polynomial factorization for the number systems that one is likely to encounter in the design of digital signal processing algorithms.
