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Accurate Rotations Based on Coefficient Scaling
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
University of Politecn Madrid.
2011 (English)In: IEEE Transactions on Circuits and Systems - II - Express Briefs, ISSN 1549-7747, Vol. 58, no 10, 662-666 p.Article in journal (Refereed) Published
Abstract [en]

This brief presents a novel approach for improving the accuracy of rotations implemented by complex multipliers, based on scaling the complex coefficients that define these rotations. A method for obtaining the optimum coefficients that lead to the lowest error is proposed. This approach can be used to get more accurate rotations without increasing the coefficient word length and to reduce the word length without increasing the rotation error. This brief analyzes two different situations where the optimization method can be applied: rotations that can be optimized independently and sets of rotations that require the same scaling. These cases appear in important signal processing algorithms such as the discrete cosine transform and the fast Fourier transform (FFT). Experimental results show that the use of scaling for the coefficients clearly improves the accuracy of the algorithms. For instance, improvements of about 8 dB in the Frobenius norm of the FFT are achieved with respect to using non-scaled coefficients.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE) , 2011. Vol. 58, no 10, 662-666 p.
Keyword [en]
Coefficient scaling, complex multiplier, error minimization, rotation
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-71783DOI: 10.1109/TCSII.2011.2164144ISI: 000296009700010OAI: diva2:453944
Funding Agencies|Ministry of Education of Spain under Formacion de Profesorado Universitario (FPU)|AP2005-0544|Spanish National Research and Development Program|TEC2008-02148|Swedish ELLIIT Program||Available from: 2011-11-04 Created: 2011-11-04 Last updated: 2015-03-11

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