Elementary Number Theory and Rader's FFT

Abstract

Abstract. This note provides a self-contained introduction to Rader's fast Fourier transform (FFT).We start by explaining the need for an additional type of FFT. The properties of the multiplicative group of the integers modulo a prime number are then developed and their relevance to the calculation of the discrete Fourier transform is explained. Rader's FFT is then derived, Rader's zero-padding technique is described, and the performance of the unpadded and the zero-padded approaches is examined. noting that each sum is now an I-term DFT that should require on the order of I 2 calculations, and noting that whenever you need terms that go past the "natural end" of a DFT you do not need to perform more calculations: instead, you find the additional terms by making use of the periodicity of the DFT. Calculating the DFT using this strategy takes on the order of I 2 L+(L−1)N operations, where the (L−1)N *

Application of Deep Neural Network with Frequency Domain Filtering in the Field of Intrusion Detection

“…Table 2 illustrates the relationship between each element in X t ij -end and each element in the original sequence X t ij , using N � 8 as an example. Te specifc implementation process can use Rader's algorithm [47][48][49][50] to obtain the correspondence between the sequence X t ij -end and the elements in the sequence X t ij , and then obtain the sequence X t ij -end . Since Rader's algorithm has been introduced in many literature works, it will not be repeated here.…”