Proceedings ArticleDOI
A multiplier-less 1-D and 2-D fast Fourier transform-like transformation using sum-of-powers-of-two (SOPOT) coefficients
S.C. Chan,P.M. Yiu +1 more
- Vol. 4, pp 755-758
TLDR
Design results show that the ML-FFT offers flexible tradeoff between arithmetic complexity and numerical accuracy in approximating the DFT, and uses the polynomial transformation to obtain similar multiplier-less approximation of 2D FFT.Abstract:
This paper proposes a new multiplier-less approximation of the 1D discrete Fourier transform (DFT) called the multiplierless fast Fourier transform-like (ML-FFT) transformation. It parameterizes the twiddle factors in conventional radix-2/sup n/ or split-radix FFT algorithms as certain rotation-like matrices and approximates the associated parameters using the sum-of-powers-of-two (SOPOT) or canonical signed digits (CSD) representations. The ML-FFT converges to the DFT when the number of SOPOT terms used increases and has an arithmetic complexity of O(Nlog/sub 2/ N) additions, where N=2/sup m/ is the transform length. Design results show that the ML-FFT offers flexible tradeoff between arithmetic complexity and numerical accuracy in approximating the DFT. Using the polynomial transformation, similar multiplier-less approximation of 2D FFT is also obtained.read more
Citations
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Journal ArticleDOI
Error Analysis and Efficient Realization of the Multiplier-Less FFT-Like Transformation (ML-FFT) and Related Sinusoidal Transformations
K. M. Tsui,S. C. Chan +1 more
TL;DR: The signal round-off error arising from internal rounding is studied, a recursive noise model is developed, and a new ML-FFT for real-valued input, called the ML-RFFT, is proposed because of the symmetry in the algorithm.
Proceedings ArticleDOI
Multiplier-less real-valued FFT-like transformation (ML-RFFT) and related real-valued transformations
S.C. Chan,K. M. Tsui +1 more
TL;DR: A new multiplier-less fast Fourier transform-like (ML-RFFT) transformation for real-valued sequences that parameterizes the twiddle factors in the conventional radix-2/sup n/ or split-radix real- valued FFT algorithm as certain rotation-like matrices and approximates the associated parameters inside these matrices by the sum-of-power- of-two (SOPOT) or canonical signed digits (CSD) representations.
Proceedings ArticleDOI
A Star Pattern Recognition Technique Based on the Binary Pattern Formed from the FFT Coefficients
TL;DR: A novel star pattern recognition technique for an LIS mode star sensor that robustly maintains the identification accuracy to 97% on the swayed and biased simulated images.
Proceedings ArticleDOI
Error analysis and complexity optimization for the multiplier-less FFT-like transformation (ML-FFT)
K. M. Tsui,S.C. Chan,K.W. Tse +2 more
TL;DR: The effect of the signal round-off errors on the accuracies of the multiplier-less fast Fourier transform-like transformation (ML-FFT) is studied.
Proceedings ArticleDOI
Fibonacci Fourier Transform and Sliding Window Filtering
TL;DR: The new Fibonacci Fourier like transform algorithms are presented, promising to be good to reduce the Gaussian noises on images and comparing with the well-known Wiener filtering.
References
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Fast Computation of Discrete Fourier Transforms Using Polynomial Transfwms
TL;DR: This paper presents two methods for computing discrete Fourier transforms (DFT) by polynomial transforms and shows that these techniques are particularly well adapted to multidimensional DFTs as well as to some one-dimensional DFT's and yield algorithms that are, in many instances, more efficient than the fast Fourier transform (FFT) or the Winograd Fourier Transform (WFTA).
Journal ArticleDOI
Fast computation of discrete Fourier transforms using polynomial transforms
Henri J. Nussbaumer,P. Quandalle +1 more
TL;DR: In this article, two polynomial transforms have been proposed for computing discrete Fourier transform (DFT) by polynomials, which are particularly well adapted to multidimensional DFT's as well as to some one-dimensional DFTs.
Journal ArticleDOI
Split vector-radix fast Fourier transform
S.C. Chan,Ka-Leung Ho +1 more
TL;DR: By introducing a general approach for constructing the fast Hartley transform (FHT) from the corresponding FFT, new vector- and split-vector-radix FHT algorithms with the same desirable properties as their FFT counterparts are obtained.
Journal ArticleDOI
An order-16 integer cosine transform
Wai-Kuen Cham,Y.T. Chan +1 more
TL;DR: It is shown that it is possible to replace the real-numbered elements of a discrete cosine transform (DCT) matrix with integers and still maintain the structure, i.e., relative magnitudes and orthogonality, among the matrix elements.
Journal ArticleDOI
The integer transforms analogous to discrete trigonometric transforms
Soo-Chang Pei,Jian-Juin Ding +1 more
TL;DR: The integer transform introduced by Cham is modified and introduced and the complete integer transform is introduced, which requires no real number multiplication operation, no matter what the forward or inverse transform.