Welcome

 

Discrete Fourier Sum

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 Laplace transform to Fourier transform.

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.

               b.   3d-SymFFT\DocList.mht

c.     3dSymmFFT2.doc

d.     Convolution in 3d.doc

10.   OZeqn.doc

11.   Sine transform.doc

12.   Test problem in detail.doc

Integrals

1.      Trap rule.doc Trap rule2.doc

2.      TransformOfGaussian.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

WOFZ.DOC

Practical Applications

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.

 

04/20/2007  01:36 PM            26,112 Fourier Sum Definitions.doc

05/12/2008  10:15 AM         1,767,936 Discrete Fourier Transform.doc

02/27/2007  04:40 AM            82,432 Fourier.doc – connects the notation with the usual physics notation and includes the delta functions.

07/29/2005  11:18 AM            51,200 Mixed Fourier.doc – part of Fourier

 

 Directory of C:\public_html\Fourier

 

04/17/2007  10:47 AM           164,352 CFOUR.doc htm– 1941 Churchill with Bob notes

05/03/2000  01:14 PM            64,000 Coddet.doc – part of another document

04/15/2003  10:27 AM            53,248 Ddho.doc  -- A driven damped harmonic oscillator violin mode

04/11/2006  08:28 AM            82,944 ddho2.doc – continuation of above

04/20/2007  01:37 PM            53,248 Delta Functions.doc htm sin(x)/x form starting from discrete Fouriert definition.

03/24/2005  10:47 AM           265,728 diffFT.doc  Similar to Ddho above

04/05/2006  08:17 PM            45,056 EMTH.DOC

06/06/2006  02:22 PM            37,376 Exp vs sine and cosine.doc

03/08/2006  10:22 PM            25,088 Harry Nyquist.doc

03/23/2006  05:17 AM           777,216 Ideal low pass filter.doc

03/08/2006  10:27 PM            33,792 IEEENyquist.doc

07/05/2005  09:05 AM           919,552 Low pass filters3.doc

08/26/2006  06:05 PM           128,000 Power.doc

09/11/2006  05:24 AM            50,176 Sine transform.doc

10/07/2003  04:48 PM            64,000 Sum of delta functions.doc

02/26/2007  02:16 PM           833,536 Test problem in detail.doc

02/16/2003  04:38 PM            19,456 Testing The FFT.doc

04/18/2007  03:12 PM            45,056 TransformOfGaussian.doc

08/02/2005  10:47 AM            55,296 Trap rule.doc

07/27/2005  04:03 PM            33,280 Trap rule2.doc

01/23/2007  10:45 PM           258,560 Violin.doc

09/04/2006  06:40 AM         1,365,504 WhiteSpace.doc

              31 File(s)      8,030,720 bytes

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 Volume in drive C is Preload

 Volume Serial Number is E073-703E

 

 Directory of C:\public_html\Fourier

 

04/18/2007  05:25 PM            59,617 Fast Fourier Transform.htm

04/20/2007  01:36 PM            17,014 Fourier Sum Definitions.htm

02/27/2007  04:40 AM            57,914 Fourier.htm

02/27/2007  04:49 AM            57,601 Nyquist.htm

03/16/2004  12:02 AM            10,818 Sinetran.htm

06/09/2003  07:54 AM            14,352 Sumortho.htm

04/18/2007  03:15 PM            47,613 Symmetric range.htm

02/26/2007  02:16 PM            20,382 Test problem in detail.htm

04/18/2007  03:12 PM            22,408 TransformOfGaussian.htm

01/23/2007  10:46 PM            84,229 Violin.htm

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