1. Discrete Fourier Transform.doc .htm(in detail)– or quickly Fourier Sum Definitions.doc .htm
Fourier.doc .htm– The
traditional Fourier integral approach.
Sumortho.htm ..\ligo\Power.htm
LaplaceTransform.doc .htm – Shows relation of
2. Delta Functions.htm -- Delta Functions.doc
3. Mixed Fourier.doc .htm letting the time or frequency interval become infinitesimal.
4. Nyquist.doc .htm – finding the function that the data points sample.
5. Codes
a. DFT code.doc .htm– a slow Fourier Transform for dealing with zero padded data using ideas detailed in Advancing the sin.doc .htm
b. Fast Fourier Transform.doc .htm
Testing
The FFT.doc
c. DFTFFTR.doc .htm - Designed to change the value of Dt in real experimental data and to also find the derivative of this data. Uses data extension, the slow Fourier transform where appropriate and the fast Fourier transform. Includes zips to the codes.
6. Symmetric range.doc .htm Using the standard FFT from –T/2 to T/2 instead of 0 to T. – The best test and code is in fftsrHth.zip Fortran code that starts and ends from data files is fftsr.for. Code that starts with DIIN(2×Nx) and ends with DIIOUT(2*Nf) is in fftsrnr.for.
7. DiscreteConvolution.doc .htm
convolution.doc
8. Phase correction - phasec\phasec~1.doc /phasec
9. multi-dimensional transforms
a. DFT2-FFT2.docx .htm Show timing for the simplest Fourier Transform, and intermediate and the FFT.
FFT2-Theory.doc .htm compares the FFT results to those analytically attained for two Gaussians.
10. OZeqn.doc
12. Test problem in detail.doc
1. Trap rule.doc Trap rule2.doc
3. Gabor windowing makes the Fourier sum à Fourier integral. It also makes D(f) àD(f,t) gabor\Gabor Transforms.doc
4. filon\Filon.doc – An integral of the polynomial interpolating BLI points.
5. SplineFT.DOC – The 4th derivative discontinuities produce a 1/f4 term in the Fourier transform.
6. Error Function and Wofz.doc
1.
fftfit.doc Fitting
data.doc FIT.doc
Exp vs sine and cosine.doc
2. Solution of a differential equation in transform space. -- Green's function diffFT.doc ddho2.doc Violin.doc
3. 15 digit Aigau data in Fourier and time domains..\aigau\AiGaussPgen\Welcome.htm
4. Fourier.zip – short set of codes.
Directory of C:\public_html\Fourier
31 File(s) 8,030,720 bytes
0 Dir(s) 121,327,562,752 bytes free
Volume in drive C is Preload
Volume Serial Number is E073-703E
Directory of C:\public_html\Fourier
14 File(s) 609,391 bytes
0 Dir(s) 121,327,558,656 bytes free