Discrete Fourier Sum

I. Fourier Sums

Discrete Fourier Transform.doc (in detail using exponential series) or quickly Fourier Sum Definitions.doc. First principles CFOUR.doc htm Starts from a sum of cosines, ends with a Fourier integral.

a) DFT code.doc “Slow transform”

b) Fast Fourier Transform.doc

(1) Testing The FFT.doc

(2) Symmetric range.doc Using the standard FFT from –T/2 to T/2 instead of 0 to T. for\symfft.zip

(3) Partial Sum.doc

c) Delta Functions.htm -- .doc

Convol\Welcome.doc
FourierFit\Welcome.htm Shows that is a least squares fit to d[i].

II. Fourier Integrals

1. MonteCarlo.docx .htm

2. hIntegralSum.doc Shows how to construct a Fourier sum from a Fourier Integral.

3. Nyquist.doc Proves that for frequency limited data a finite number of time steps can reproduce the underlying function everywhere

a. ContFreq.doc

b. Trap rule.doc Trap rule2.doc

c. TransformOfGaussian.doc

(1) GaussTimeFreq.doc

(2) GaussFreqTime.doc

d. filon\Filon.doc – An integral of the polynomial interpolating BLI points.

e. SplineFT.DOC – The 4^th derivative discontinuities produce a 1/f⁴ term in the Fourier transform.

4. Phase correction - phasec\phasec~1.doc /phasec

III. 3d-SymFFT\DocList.mht – multi-dimensional transforms

a. 3dSymmFFT2.doc

b. Convolution in 3d.doc

IV. ..\ligo\Power.htm

V. Sine transform.doc

VI. Test problem in detail.doc

Gabor

1. Gabor windowing makes the Fourier sum à Fourier integral. It also makes D(f) àD(f,t) gabor\Gabor Transforms.doc

Theory

1. Nyquist.doc . Ideal low pass filter.doc

2. PeriodBC Born-Von Karmen.doc. Condensed matter boundary conditions make solid state wave functions periodic.

3. Numerical Hartree Fock

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.

Document list

05/28/2008 10:43 PM 65,024 Advancing the sin.doc advsin.zip, advsin2.zip, Inteltdft.zip

03/07/2006 02:20 PM 80,384 aiGausst.doc

06/20/2008 09:56 PM 48,640 ArgMod.doc

06/15/2008 12:33 AM 339,456 BobFast.doc fftBob6-15-08.zip

04/17/2007 10:47 AM 164,352 CFOUR.doc

05/03/2000 01:14 PM 64,000 Coddet.doc

07/16/2008 04:20 PM 153,088 ContFreq.doc

12/09/2006 05:09 PM 59,392 ConvolTwoGaussians.doc

03/04/2004 09:50 PM 99,328 convolution.doc

05/17/2008 09:13 PM 210,944 Copy of Discrete Fourier Transform.doc

04/15/2003 10:27 AM 53,248 Ddho.doc

04/11/2006 08:28 AM 82,944 ddho2.doc

04/20/2007 01:37 PM 53,248 Delta Functions.doc

05/27/2008 12:14 AM 158,720 DFT code.doc for\dft1.zip, cpp\Cmod.zip

05/20/2008 03:44 PM 112,562 Dft1.docx

03/24/2005 10:47 AM 265,728 diffFT.doc

08/04/2008 11:55 AM 148,480 Discrete Fourier Transform.doc

05/20/2008 04:15 PM 67,584 DiscreteConvolution.doc

04/05/2006 08:17 PM 45,056 EMTH.DOC referred to in Ddho and Violin

07/07/2008 03:40 PM 85,504 ERRFC.doc

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

08/04/2008 12:31 PM 36,864 ExtendingFrequency.doc

05/23/2008 08:49 AM 124,416 Fast Fourier Transform.doc

07/18/2008 08:10 PM 175,616 Finite Integral Fourier Transform.doc (does fit uses integral orthogonality)

08/06/2002 12:10 PM 63,488 FIT.doc (old not very related)

05/15/2008 08:10 AM 29,184 Fourier Sum Definitions.doc

05/21/2008 06:39 PM 78,848 Fourier.doc

07/26/2005 04:51 PM 25,600 GaussFreqTime.doc

06/03/2006 10:40 PM 78,336 GaussTimeFreq.doc

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

07/30/2008 06:29 PM 60,416 hIntegralSum.doc

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

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

05/14/2008 10:18 PM 26,624 Integral Orthogonality.doc

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

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

02/27/2007 04:48 AM 119,808 Nyquist.doc

04/18/2007 09:50 AM 420,352 OZeqn.doc

06/10/2008 03:38 PM 37,888 Partial Sum.doc

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

06/19/2008 01:41 PM 331,776 PressBob12-2.doc

07/31/2008 01:59 PM 55,296 RealityCondition.doc

05/24/2008 11:52 PM 48,128 SCRATCH.doc

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

08/26/2006 07:16 AM 145,920 SplineFT.DOC

06/13/2008 07:24 AM 38,912 Square of a function.doc

05/18/2008 09:50 AM 27,648 Sum 1 to N.doc

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

05/18/2008 09:38 AM 62,464 Sum.doc

04/18/2007 03:15 PM 183,296 Symmetric range.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

08/04/2008 12:12 PM 122,368 ZeroPadding.doc

08/04/2008 01:02 PM 136,704 ZeroPaddingF.doc