Fourier Transform / News: Recent posts

Error corrections in the Fourier Transform article

Corrected few typos and one major mistake in Discrete Cosine Transform topic.
Updated article is on the same place:
http://arkadianalysis.sourceforge.net/Fourier.pdf

Posted by Arkadi 2007-12-20

LPC - Linear Predictive Coding

Published first draft with detailed explanation on LPC. Was choosen the shortest way to show why Levinson-Durbin Recursion is right.

See it here:
http://arkadianalysis.sourceforge.net/LPC.pdf

Posted by Arkadi 2006-05-04

Correction in DIT FFT/FCT/FST transform document

The corrected mistake could lead to computing only half coofecients on each recursion step. The result could be all the vector computed wrong.

The document was checked more carefully and now direct implementation is computing right values.
See corected document at
http://arkadianalysis.sourceforge.net/FFT.pdf

TODO: I must check it again.

Posted by Arkadi 2005-06-11

Fast Discrete Cosine and Sine Transforms

Described FCT and FST algorithmes of Radix 2 with usage of only "Decimation In Time" approach.

The document is here:
http://arkadianalysis.sourceforge.net/FFT.pdf

Posted by Arkadi 2005-05-09

Discrete Fourier Transform prove

Two issues are resolved:
1. Strict prove validity of Discrete Fourier Transform.
2. Some of ambiquity in Fourier Integral prove is repaired.
http://arkadianalysis.sourceforge.net/Fourier.pdf

All the set must be yet revised for mistakes and clarifications.

Posted by Arkadi 2005-01-19

Orthogonality of Complex Continuous Functions

Proved Orthogonality of Complex Continuous Functions.
The document is updated and new files are available.
http://arkadianalysis.sourceforge.net/tools.html

Posted by Arkadi 2004-12-13

Errors correction in documentation

Corrected several typing and logic errors in math documents.

Posted by Arkadi 2004-12-04

Fast Fourier Transform of Radix 2 for Complex data

Document with detailed prove of Fast Fourier Transform of Radix 2 for Complex data.
Open Office: http://arkadianalysis.sourceforge.net/FFT.sxw
PDF: http://arkadianalysis.sourceforge.net/FFT.pdf

Posted by Arkadi 2004-11-26

Complex Multidimentional vectors Orthogonality

Document with detailed motivation for Complex Multidimentional vectors Orthogonality to be valid.
Open Office: http://arkadianalysis.sourceforge.net/Orthogonality.sxw
PDF: http://arkadianalysis.sourceforge.net/Orthogonality.pdf

Posted by Arkadi 2004-11-26

Corrected errors in prove of Fourier Transform.

Conception "Set of Pairwise Orthogonal functions" is used as it must be.
In previous version two sets of functions where used. It is mathematically right, however it will stop farther development of the subject.

Posted by Arkadi 2004-10-08

Document with detailed prove of Fourier Transform

Available new document with detailed prove of Fourier Transform.
The original is writen with Open Office: http://arkadianalysis.sourceforge.net/Fourier.sxw
Else PDF version is available:
http://arkadianalysis.sourceforge.net/Fourier.pdf
And HTML version:
http://arkadianalysis.sourceforge.net/Fourier/Fourier.html

Posted by Arkadi 2004-09-15