Aimed at solving the problems of Precision code’s complex acquisition procedures and its long acquisition time in satellite navigation, this paper makes an architecture analysis of the commonly used direct acquisition algorithms of Precision code, making an improvement of the common local pseudorandom code based glide Fast Fourier Transform acquisition architecture. Besides those, it also puts ...

AMS Subject Classi cation: 20-04, 05C25, 20C30 Rockmore was supported in part by a National Science Foundation Mathematical Sciences Postdoctoral Fellowship. We study the complexity of performing Fourier analysis for the group SL2(Fq), where Fq is the finite field of q elements. Direct computation of a complete set of Fourier transforms for a complex-valued function f on SL2(Fq) requires q6 ope...

It seems likely that improvements in arithmetic speed will continue to outpace advances in communications bandwidth. Furthermore, as more and more problems are working on huge datasets, it is becoming increasingly likely that data will be distributed across many processors because one processor does not have sufficient storage capacity. For these reasons, we propose that an inexact DFT such as ...

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...