The object of this chapter is to briefly summarize the main properties of the discrete Fourier
transform (DFT) and to present various fast DFT computation techniques known collectively …

The pioneering work of French mathematician Pierre de Fermat has attracted the attention of
mathematicians for over 350 years. This book was written in honor of the 400th anniversary …

Discrete transforms are introduced and are defined in a ring of polynomials. These
polynomial transforms are shown to have the convolution property and can be computed in …

Recently, the quadratic residue number system (QRNS) has been introduced [6],[7] which
allows the multiplication of complex integers with two real multiplications. The restriction is …

Complex Mersenne Transforms are defined in a ring of integers modulo a Mersenne or
pseudo-Mersenne number and can be computed without multiplications. It is shown that …

In this paper pseudo Fermat number transforms (FNT's) are discussed. These transforms are
defined in a ring of integers modulo an integer submultiple of a pseudo Fermat number, and …

Very recently, the quadratic residue number system (QRNS) has been introduced [8],[9]. It is,
in fact, a rediscovery of earlier work [29]. The QRNS is obtained from a mapping of Gaussian …

It has been known for a long time that quadratic modular number codes admit an unusual
representation of complex numbers which leads to complete decoupling of the real and …

Publisher Summary This chapter discusses the application of number theory to the intensive
computations required in many digital signal processing (DSP) systems. DSP system is …

Modulo arithmetic modulo a prime integer have many interesting properties. Such properties
are found in standard books on number theory. Some properties are especially of interest to …