FFTPACK4
Fast Fourier Transform

FFTPACK4 is a C library which computes Fast Fourier Transforms, by Paul Swarztrauber;

Special features include:

• real or complex data can be handled;
• separate routines for forward analysis (data => Fourier coefficients) and backward analysis (Fourier coefficients => data);
• sine and cosine transform routines;
• quarter wave sine and cosine transform routines;
• the amount of data is NOT required to be a power of 2.

Routines in the library come in groups of three:

• an initialization routine;
• the forward computational routine (data to FFT coefficients);
• the backward computational routine (FFT coefficients to data).

The following table groups the routines:

Initialization	Forward	Backward	Purpose
CFFTI	CFFTF	CFFTB	FFT for complex data
COSQI	COSQF	COSQB	Even function 1D quarter-cosine FFT for real data
COSTI	COST	COST	Even function 1D cosine FFT for real data
EZFFTI	EZFFTF	EZFFTB	FFT for real data
RFFTI	RFFTF	RFFTB	FFT for real data
SINQI	SINQF	SINQB	Even function 1D quarter-sine FFT for real data
SINTI	SINT	SINT	Even function 1D sine FFT for real data

Licensing:

All the changes made by Andrew Fernandes from the original FFTPACK fall under the following BSD-style open-source license:

  Copyright (c) 2005, Andrew Fernandes (andrew@fernandes.org);
  All rights reserved.
   
  Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions
  are met:
   
  - Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.
  
  - Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer in the
  documentation and/or other materials provided with the distribution.
  
  - Neither the name of the North Carolina State University nor the
  names of its contributors may be used to endorse or promote products
  derived from this software without specific prior written permission.
   
  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
  FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
  COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
  BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  POSSIBILITY OF SUCH DAMAGE.
      

Languages:

FFTPACK4 is available in a C version.

Related Data and Programs:

FFT_OPENMP, a C program which demonstrates the computation of a Fast Fourier Transform (FFT) in parallel, using OpenMP.

FFT_SERIAL, a C program which demonstrates the computation of a Fast Fourier Transform (FFT), and is intended as a starting point for implementing a parallel version.

FFTPACK5, a FORTRAN90 library which implements the Fast Fourier Transform (FFT) by Paul Swarztrauber and Dick Valent;

FFTW3, C programs which illustrate the use of the FFTW3 library for Fast Fourier Transforms (FFT), by Matteo Frigo and Steven Johnson.

SFTPACK, a C library which implements the slow Fourier transform, intended as a teaching tool and comparison with the Fast Fourier Transform (FFT).

Author:

The original Fortran77 version of this code was written by Dick Valent and Paul Swarztrauber, of the National Center for Atmospheric Research (NCAR).

The translation to C was done by Andrew Fernandes.

Reference:

1. William Briggs, Van Emden Henson,
   The DFT: An Owner's Manual for the Discrete Fourier Transform,
   SIAM, 1995,
   ISBN13: 978-0-898713-42-8,
   LC: QA403.5.B75.
2. Elbert Brigham,
   The Fast Fourier Transform and Its Applications,
   Prentice-Hall, 1988,
   ISBN: 0133075052,
   LC: QA403.B74.
3. Bill Buzbee,
   The SLATEC Common Math Library,
   in Sources and Development of Mathematical Software,
   edited by Wayne Cowell,
   Prentice-Hall, 1984,
   ISBN: 0-13-823501-5,
   LC: QA76.95.S68.
4. Eleanor Chu, Alan George,
   Inside the FFT Black Box,
   CRC Press,
   ISBN: 0849302706,
   LC: QA403.5C5.
5. David Kahaner, Cleve Moler, Steven Nash,
   Numerical Methods and Software,
   Prentice Hall, 1989,
   ISBN: 0-13-627258-4,
   LC: TA345.K34.
6. Paul Swarztrauber,
   Symmetric FFT's,
   Mathematics of Computation,
   Volume 47, Number 175, July 1986, pages 323-346.
7. Paul Swarztrauber,
   Vectorizing the Fast Fourier Transforms,
   in Parallel Computations,
   edited by Garry Rodrigue,
   Academic Press, 1982,
   ISBN: 0125921012,
   LC: QA76.6.P348.
8. Paul Swarztrauber,
   Fast Fourier Transform Algorithms for Vector Computers,
   Parallel Computing,
   Volume 1, Number 1, August 1984, pages 45-63.

Source Code:

• fftpack4.c, the source code.
• fftpack4.h, the include file.
• fftpack4_precision.h, an include file which can be used to specify the precision of the library at compile time.

Examples and Tests:

• fftpack4_test.c, a sample calling program.
• fftpack4_test.txt, the output from a run of the sample program.

List of Routines:

• CFFTB: complex backward fast Fourier transform.
• CFFTF: complex forward fast Fourier transform.
• CFFTI: initialization for CFFTB and CFFTF.
• COSQB: real backward cosine quarter wave transform.
• COSQF: real forward cosine quarter wave transform.
• COSQI: initialization for COSQB and COSQF.
• COST: real forward/backward cosine transform.
• COSTI: initialization for COST.
• EZFFTB: real backward fast Fourier transform.
• EZFFTF: real forward fast Fourier transform.
• EZFFTI: initialization for EZFFTB and EZFFTF.
• RFFTB: real backward fast Fourier transform.
• RFFTF: real forward fast Fourier transform.
• RFFTI: initialization for RFFTB and RFFTF.
• SINQB: real backward sine quarter wave transform.
• SINQF: real forward sine quarter wave transform.
• SINQI: initialization for SINQB and SINQF.
• SINB: real forward/backward sine transform.
• SINTI: initialization for SINT.

You can go up one level to the C source codes.