ABSTRACT
Among all the ingredients that go into the construction of good algorithms for digital signal processing, the key ones are number theory, polynomial algebra, the Chinese remainder theorem, and field theory. Aspects of number theory that pertain to the digital signal processing of data sequences defined over the infinite fields of rational numbers, https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315141312/eb9507de-5963-43d1-b207-f60a521e202b/content/z.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>, real numbers, https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315141312/eb9507de-5963-43d1-b207-f60a521e202b/content/re.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>, complex rational numbers, https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315141312/eb9507de-5963-43d1-b207-f60a521e202b/content/cz.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>, and complex numbers, https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315141312/eb9507de-5963-43d1-b207-f60a521e202b/content/c.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>, were described in Chapter 2. Chapter 3 dealt with the polynomial algebra and the CRT-P for data sequences defined over an arbitrary field. Based on these ideas, the basic formulation of the digital signal processing algorithms for computing cyclic and acyclic convolution was presented in Chapter 4.
