NDLI: Novel Reversible Integer Fourier Transform With Control Bits

Content Provider	IEEE Xplore Digital Library
Author	Grigoryan, A.M.
Copyright Year	1991
Abstract	This paper presents a novel concept of the reversible integer discrete Fourier transform (RiDFT) of order 2^r, r > 2, when the transform is split by the paired representation into a minimum set of short transforms, i.e., transforms of orders 2^k, 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.
Sponsorship	IEEE Signal Processing Society
Starting Page	5267
Ending Page	5276
Page Count	10
File Size	474085
File Format	PDF
ISSN	1053587X
Volume Number	55
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-11-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fourier transforms Discrete Fourier transforms Discrete transforms Discrete wavelet transforms Fast Fourier transforms Discrete cosine transforms Image coding Frequency Computational complexity paired transform Discrete Fourier transform integer transforms
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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