SINE_TRANSFORM
A Discrete Fourier Transform for Real Data

SINE_TRANSFORM is a FORTRAN77 library which demonstrates some simple properties of the discrete sine transform for real data.

The code is not optimized in any way, and is intended instead for investigation and education.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

SINE_TRANSFORM is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

FFT_SERIAL, a FORTRAN77 program which demonstrates the computation of a Fast Fourier Transform, and is intended as a starting point for implementing a parallel version.

FFTPACK5.1, a FORTRAN77 library which implements the Fast Fourier Transform by Paul Swarztrauber and Dick Valent;

HAAR, a FORTRAN77 library which computes the Haar transform of data.

SFTPACK, a FORTRAN77 library which implements the "slow" Fourier transform, intended as a teaching tool and comparison with the fast Fourier transform.

WALSH, a FORTRAN77 library which implements versions of the Walsh and Haar transforms.

WAVELET, a FORTRAN77 library which does some simple calculations with wavelet transforms;

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. Eleanor Chu, Alan George,
   Inside the FFT Black Box,
   CRC Press,
   ISBN: 0849302706,
   LC: QA403.5C5.

Source Code:

• sine_transform.f, the source code.
• sine_transform.sh, BASH commands to compile the source code.

Examples and Tests:

• sine_transform_prb.f, a sample calling program.
• sine_transform_prb.sh, BASH commands to compile and run the sample program.
• sine_transform_prb_output.txt, the output file.
• sine_transform_prb03.png, a PNG image comparing the function and interpolant.
• sine_transform_prb04.png, a PNG image comparing the function and interpolant.

List of Routines:

• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• SINE_TRANSFORM_DATA does a sine transform on a vector of data.
• SINE_TRANSFORM_FUNCTION does a sine transform on functional data.
• SINE_TRANSFORM_INTERPOLANT evaluates the sine transform interpolant.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN77 source codes.