Lewis, and Welch in this issue The fast Fourier transform (FFT) is a method. efficiently As mentioned in the Introduction, the FFT is an algorithm that makes. A fast Fourier transform (FFT) is an algorithm to compute the DFT and its The basic ideas were popularized in 1965, but some FFTs had been previously. This document is a very brief introduction to sound analysis principles. It is mainly F...

Computing the discrete Fourier transform is one of the most important in applied computer science, with applications in fields as diverse as seismology, signal analysis, and various branches of engineering. A great many algorithms exist for quickly computing different variations of the transform – fast Fourier transforms, or FFTs. Because of their practical importance, even small improvements t...

In ISSAC 2017, van der Hoeven and Larrieu showed that evaluating a polynomial P ∈ Fq [x] of degree < n at all n-th roots of unity in Fqd can essentially be computed d-time faster than evaluating Q ∈ Fqd [x] at all these roots, assuming Fqd contains a primitive n-th root of unity [vdHL17a]. Termed the Frobenius FFT, this discovery has a profound impact on polynomial multiplication, especially fo...

In this paper, a concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has properties that it is an integer-to-integer mapping, power adaptable and also reversible. Lifting scheme is used to approximate complex multiplications appearing in the FFT lattice struct...

This paper extends the concepts of the Sparse Fast Fourier Transform (sFFT) Algorithm introduced in [1] to work with two dimensional (2D) data. The 2D algorithm requires several generalizations to multiple key concepts of the 1D sparse Fourier transform algorithm. Furthermore, several parameters needed in the algorithm are optimized for the reconstruction of sparse image spectra. This paper add...

The class of second-order curvilinear gratings consists of all the curvilinear gratings that are obtained by second-order spatial transformations of periodic gratings. It includes, for example, circular, elliptic, and hyperbolic gratings as well as circular, elliptic, and hyperbolic zone plates. Such structures occur quite frequently in optics, and their Fourier transforms may arise, for instan...

We give a discussion of harmonic analysis on finite abelian groups, emphasizing various ways in which the structure of the group is encoded on various spaces of functions, ways in which the Fourier transform detects and preserves these structures. We discuss the major tools, like convolutions and Fourier transforms, along with some fundamental theorems, like the Plancheral, Parseval, Fourier in...

The following paper presents the results of tests conducted by the author in the field of verification of influence of JPEG lossy compression on the robustness of data hiding methods used for the colour image which has been transformed to the frequency domain. The data have been embedded to the Fourier magnitude spectrum of the image. The possibility of decoding the hidden data with two embeddi...

An efficient algorithm for computing the one-dimensional partial fast Fourier transform fj = ∑c(j) k=0 e Fk is presented. Naive computation of the partial fast Fourier transform requires O(N) arithmetic operations for input data of length N . Unlike the standard fast Fourier transform, the partial fast Fourier transform imposes on the frequency variable k a cutoff function c(j) that depends on ...