# The regular Fourier matrices and nonuniform fast Fourier transforms

## Abstract

For any triple of positive integers (m,N,q), the matrix F(m,N,q), called the (m,N,q)-regular Fourier matrix, is defined. The regular Fourier matrices F(m,N,q) are then applied to set up new algorithms for nonuniform fast Fourier transforms. Numerical results show that the accuracies obtained by the algorithms are much better than previously reported results with the same computation complexity. The algorithms require O(N {center{underscore}dot} log{sub 2}N) arithmetic operations, where N is the number of data points.

- Authors:

- Publication Date:

- Research Org.:
- New Mexico State Univ., Las Cruces, NM (US)

- Sponsoring Org.:
- Environmental Protection Agency; Sandia National Laboratories; National Science Foundation (NSF)

- OSTI Identifier:
- 20015656

- Resource Type:
- Journal Article

- Journal Name:
- SIAM Journal on Scientific Computing

- Additional Journal Information:
- Journal Volume: 21; Journal Issue: 1; Other Information: PBD: Sep 1999; Journal ID: ISSN 1064-8275

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; FOURIER TRANSFORMATION; ALGORITHMS; MATRICES; PERFORMANCE

### Citation Formats

```
Nguyen, N., and Liu, Q.H.
```*The regular Fourier matrices and nonuniform fast Fourier transforms*. United States: N. p., 1999.
Web. doi:10.1137/S1064827597325712.

```
Nguyen, N., & Liu, Q.H.
```*The regular Fourier matrices and nonuniform fast Fourier transforms*. United States. doi:10.1137/S1064827597325712.

```
Nguyen, N., and Liu, Q.H. Wed .
"The regular Fourier matrices and nonuniform fast Fourier transforms". United States. doi:10.1137/S1064827597325712.
```

```
@article{osti_20015656,
```

title = {The regular Fourier matrices and nonuniform fast Fourier transforms},

author = {Nguyen, N. and Liu, Q.H.},

abstractNote = {For any triple of positive integers (m,N,q), the matrix F(m,N,q), called the (m,N,q)-regular Fourier matrix, is defined. The regular Fourier matrices F(m,N,q) are then applied to set up new algorithms for nonuniform fast Fourier transforms. Numerical results show that the accuracies obtained by the algorithms are much better than previously reported results with the same computation complexity. The algorithms require O(N {center{underscore}dot} log{sub 2}N) arithmetic operations, where N is the number of data points.},

doi = {10.1137/S1064827597325712},

journal = {SIAM Journal on Scientific Computing},

issn = {1064-8275},

number = 1,

volume = 21,

place = {United States},

year = {1999},

month = {9}

}

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