DocumentCode :
1112291
Title :
A two-stage representation of DFT and its applications
Author :
Ersoy, Okan K.
Author_Institution :
Purdue University, West Lafayette, IN
Volume :
35
Issue :
6
fYear :
1987
fDate :
6/1/1987 12:00:00 AM
Firstpage :
825
Lastpage :
831
Abstract :
A two-stage representation in terms of preprocessing and postprocessing of DFT is developed by vector transformation of sines and cosines into new basis functions using Möbius inversion of number theory. The preprocessing matrix, with elements 1, -1, and 0, is obtained by replacing 
and 
by 
and 
, respectively, where 
is the bipolar rectangular wave function. The postprocessing matrix is block diagonal where each block is a circular correlation and consists of the new basis functions. The two-stage representation has been found very useful in applications such as parallel implementation of DFT and signal/image recognition.
and by and , respectively, where is the bipolar rectangular wave function. The postprocessing matrix is block diagonal where each block is a circular correlation and consists of the new basis functions. The two-stage representation has been found very useful in applications such as parallel implementation of DFT and signal/image recognition.Keywords :
Acoustics; Discrete Fourier transforms; Equations; Frequency; Helium; Parallel algorithms; Signal processing; Speech processing; Vectors; Wave functions;
fLanguage :
English
Journal_Title :
Acoustics, Speech and Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
0096-3518
Type :
jour
DOI :
10.1109/TASSP.1987.1165202
Filename :
1165202
Link To Document :
