liu.seSearch for publications in DiVA
Change search
ReferencesLink to record
Permanent link

Direct link
Low-Complexity Constant Multiplication Based on Trigonometric Identities with Applications to FFTs
Linköping University, Department of Electrical Engineering. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Electronics System. Linköping University, The Institute of Technology.ORCID iD: 0000-0003-3470-3911
2011 (English)In: IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, ISSN 0916-8508, E-ISSN 1745-1337, Vol. E94A, no 11, 2361-2368 p.Article in journal (Refereed) Published
Abstract [en]

In this work we consider optimized twiddle factor multipliers based on shift-and-add-multiplication. We propose a low-complexity structure for twiddle factors with a resolution of 32 points. Furthermore, we propose a slightly modified version of a previously reported multiplier for a resolution of 16 points with lower round-off noise. For completeness we also include results on optimal coefficients for eight-points resolution. We perform finite word length analysis for both coefficients and round-off errors and derive optimized coefficients with minimum complexity for varying requirements.

Place, publisher, year, edition, pages
Institute of Electronics, Information and Communication Engineers , 2011. Vol. E94A, no 11, 2361-2368 p.
Keyword [en]
complex multiplier, FFT, constant multiplication, shift-and-add multiplication
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-72819DOI: 10.1587/transfun.E94.A.2361ISI: 000296673300038OAI: diva2:462835
Funding Agencies|Higher Education Commission, Pakistan||Linkoping University, Sweden||Available from: 2011-12-08 Created: 2011-12-08 Last updated: 2015-03-11
In thesis
1. Optimization of Rotations in FFTs
Open this publication in new window or tab >>Optimization of Rotations in FFTs
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The aims of this thesis are to reduce the complexity and increasethe accuracy of rotations carried out inthe fast Fourier transform (FFT) at algorithmic and arithmetic level.In FFT algorithms, rotations appear after every hardware stage, which are alsoreferred to as twiddle factor multiplications.

At algorithmic level, the focus is on the development and analysisof FFT algorithms. With this goal, a new approach based on binary tree decompositionis proposed. It uses the Cooley Tukey algorithm to generate a large number ofFFT algorithms. These FFT algorithms have identical butterfly operations and data flow but differ inthe value of the rotations. Along with this, a technique for computing the indices of the twiddle factors based on the binary tree representation has been proposed. We have analyzed thealgorithms in terms of switching activity, coefficient memory size, number of non-trivial multiplicationsand round-off noise. These parameters have impact on the power consumption, area, and accuracy of the architecture.Furthermore, we have analyzed some specific cases in more detail for subsets of the generated algorithms.

At arithmetic level, the focus is on the hardware implementation of the rotations.These can be implemented using a complex multiplier,the CORDIC algorithm, and constant multiplications. Architectures based on the CORDIC and constant multiplication use shift and add operations, whereas the complex multiplication generally uses four real multiplications and two adders.The sine and cosine coefficients of the rotation angles fora complex multiplier are normally stored in a memory.The implementation of the coefficient memory is analyzed and the best possible approaches are analyzed.Furthermore, a number of twiddle factor multiplication architectures based on constant multiplications is investigated and proposed. In the first approach, the number of twiddle factor coefficients is reduced by trigonometric identities. By considering the addition aware quantization method, the accuracy and adder count of the coefficients are improved. A second architecture based on scaling the rotations such that they no longer have unity gain is proposed. This results in twiddle factor multipliers with even lower complexity and/or higher accuracy compared to the first proposed architecture.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. 49 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1423
Discrete Fourier transform, Fast Fourier transform, twiddle factor multiplication
National Category
Signal Processing
urn:nbn:se:liu:diva-74702 (URN)978-91-7519-973-3 (ISBN)
Public defence
2012-03-01, Visionen, B-huset, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Available from: 2012-02-07 Created: 2012-02-05 Last updated: 2015-03-11Bibliographically approved

Open Access in DiVA

fulltext(265 kB)480 downloads
File information
File name FULLTEXT01.pdfFile size 265 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Qureshi, FahadGustafsson, Oscar
By organisation
Department of Electrical EngineeringThe Institute of TechnologyElectronics System
In the same journal
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
Engineering and Technology

Search outside of DiVA

GoogleGoogle Scholar
Total: 480 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 60 hits
ReferencesLink to record
Permanent link

Direct link