SINE_TRANSFORM
A Discrete Fourier Transform for Real Data

SINE_TRANSFORM is a MATLAB 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. p

Related Data and Programs:

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

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

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

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

WAVELET, a MATLAB 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:

• r8vec_uniform_01.m, fills an R8VEC with unit uniform pseudorandom numbers.
• sine_transform_data.m, does a sine transform on a vector of data.
• sine_transform_function.m, does a sine transform on functional data.
• sine_transform_interpolant.m, evaluates the sine transform interpolant.
• timestamp.m, prints the current YMDHMS date as a time stamp.

Examples and Tests:

• sine_transform_test.m, calls all the tests;
• sine_transform_test_output.txt, the output file.
• sine_transform_test01.m, demonstrates that the transform is its own inverse.
• sine_transform_test02.m, uses the functional form of the transform.
• sine_transform_test03.m, evaluates the sine transform interpolant for a polynomial.
• sine_transform_test03.png, a PNG image comparing the function and interpolant.
• sine_transform_test04.m, evaluates the sine transform interpolant for a sum of cosines.
• sine_transform_test04.png, a PNG image comparing the function and interpolant.
• poly5.m, evaluates a particular fifth-degree polynomial;
• cosine_sum.m, evaluates a function which is the sum of cosines.

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