By Topic

Novel Reversible Integer Fourier Transform With Control Bits

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Artyom M. Grigoryan ; Univ. of Texas at San Antonio, San Antonio

This paper presents a novel concept of the reversible integer discrete Fourier transform (RiDFT) of order 2r, r > 2, when the transform is split by the paired representation into a minimum set of short transforms, i.e., transforms of orders 2k, k < r. By means of the paired transform the signal is represented as a set of short signals which carry the spectral information of the signal at specific and disjoint sets of frequencies. The paired transform-based fast Fourier transform (FFT) involves a few operations of multiplication that can be approximated by integer transforms. Examples of 1-point transforms with one control bit are described. Control bits allow us to invert such approximations. Two control bits are required to perform the 8-point RiDFT, and 12 (or even 8) bits for the 16-point RiDFT of real inputs. The proposed forward and inverse RiDFTs are fast, and the computational complexity of these transforms is comparative with the complexity of the FFT. The 8-point direct and inverse RiDFTs are described in detail.

Published in:

IEEE Transactions on Signal Processing  (Volume:55 ,  Issue: 11 )