Uniform error estimates for nonequispaced fast Fourier transforms
نویسندگان
چکیده
Abstract In this paper, we study the error behavior of nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on convenient choice a compactly supported window function. So far, various functions have been used and new recently proposed. We present novel estimates for NFFT with supported, continuous derive rules from parameters involved in NFFT. The constant function depends oversampling factor truncation parameter.
منابع مشابه
Fast Fourier Transforms for Nonequispaced Data
A group of algorithms is presented generalizing the fast Fourier transform to the case of nonin-teger frequencies and nonequispaced nodes on the interval [-r, r]. The schemes of this paper are based on a combination of certain analytical considerations with the classical fast Fourier transform and generalize both the forward and backward FFTs. Each of the algorithms requires O(N log N + N-log(I...
متن کاملNumerical stability of nonequispaced fast Fourier transforms
This paper presents some new results on numerical stability for multivariate fast Fourier transform of nonequispaced data (NFFT). In contrast to fast Fourier transform (of equispaced data), the NFFT is an approximate algorithm. In a worst case study, we show that both approximation error and roundoff error have a strong influence on the numerical stability of NFFT. Numerical tests confirm the t...
متن کاملChapter 1 Fast Fourier Transforms for Nonequispaced Data: a Tutorial
In this section, we consider approximative methods for the fast computation of multivariate discrete Fourier transforms for nonequi-spaced data (NDFT) in the time domain and in the frequency domain. In particular, we are interested in the approximation error as function of the arithmetic complexity of the algorithm. We discuss the robustness of NDFT{algorithms with respect to roundoo errors and...
متن کاملParticle Simulation Based on Nonequispaced Fast Fourier Transforms
The fast calculation of long-range interactions is a demanding problem in particle simulation. The main focus of our approach is the decomposition of the problem in building blocks and present efficient numerical realizations for these blocks. For that reason we recapitulate the fast Fourier transform at nonequispaced nodes and the fast summation method. We describe the application of these alg...
متن کاملThe Nonequispaced Fast Fourier Transform: Implementation and Error Analysis
The Fast Fourier Transform (FFT) reduces the number of computations required for the straightforward calculation of the discrete Fourier transform. For a one-dimensional signal of length N , this provides a reduction in complexity from O(N) to O(N log2 N) operations. Recently, fast algorithms have been introduced for discrete Fourier transforms on nonequispaced data sets (NDFT). These algorithm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Sampling theory, signal processing, and data analysis
سال: 2021
ISSN: ['2730-5724', '1530-6429', '2730-5716']
DOI: https://doi.org/10.1007/s43670-021-00017-z