NDLI: Integer fast Fourier transform

Content Provider	IEEE Xplore Digital Library
Author	Oraintara, S. Chen, Y.J. Nguyen, T.Q.
Copyright Year	1991
Abstract	A concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has the properties that it is an integer-to-integer mapping, is power adaptable and is reversible. The lifting scheme is used to approximate complex multiplications appearing in the FFT lattice structures where the dynamic range of the lifting coefficients can be controlled by proper choices of lifting factorizations. Split-radix FFT is used to illustrate the approach for the case of 2/sup N/-point FFT, in which case, an upper bound of the minimal dynamic range of the internal nodes, which is required by the reversibility of the transform, is presented and confirmed by a simulation. The transform can be implemented by using only bit shifts and additions but no multiplication. A method for minimizing the number of additions required is presented. While preserving the reversibility, the IntFFT is shown experimentally to yield the same accuracy as the FxpFFT when their coefficients are quantized to a certain number of bits. Complexity of the IntFFT is shown to be much lower than that of the FxpFFT in terms of the numbers of additions and shifts. Finally, they are applied to noise reduction applications, where the IntFFT provides significantly improvement over the FxpFFT at low power and maintains similar results at high power.
Sponsorship	IEEE Signal Processing Society
Starting Page	607
Ending Page	618
Page Count	12
File Size	261665
File Format	PDF
ISSN	1053587X
Volume Number	50
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-03-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fast Fourier transforms Discrete Fourier transforms Dynamic range Noise reduction Fourier transforms Lattices Upper bound Digital signal processing Convolution
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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