An Approach in Designing 16-point DFT with Decimation in Time based on Rademacher Functions
Keywords:
8-Point DFT, Decimation In Time, Fourier Transforms, Walsh Transform,Abstract
This paper presents a circuit design for 16-point DFT algorithm with Decimation in Time based on products of Rademacher functions. The designed circuit is constructed from two 8-point DFT and four 2-point DFT. However, the operation of the design circuit is different. It utilised the advantages of the similarity of Fourier transforms, and Rademacher functions. Therefore, the proposed design is constructed from previously designed 8-point DFT which is based on products of Rademacher functions. Some analysis of the type of numbers, internal connections and the complex conjugate of the results to achieve the more efficient circuit has been made. Therefore, instead of eight, the proposed design requires only five 2-point DFTs. Therefore, six output results of the design 16-point DFT have been removed since they are equal regarding magnitude to the other results, but six negative circuits are required as compensation. Therefore, the previously designed circuit of 8- point DFT has been replaced with the new circuit design. This circuit is specially designed for non-standalone used; the circuit must be integrated inside the proposed 16-point DFT.References
P. Duhamel, and M. Vetterli, “Fast Fourier Transforms: a tutorial, review and a state of the art,” Trans. Signal Processing, vol. 19, no. 4, pp. 259-299, April 1990.
J.W. Cooley and J.W. Tukey, "An Algorithm for the Machine Calculation of Complex Fourier Series," Math. Comp., Vol. 19, pp. 297-301, April 1965.
S. Boussakta, and A. G. J. Holt, “Fast algorithm for calculation of both Walsh-Hadamard and Fourier transforms (FWFTs),” Electron. Letter, vol. 25, no. 20, pp. 1352-1354, 1989.
Monir T. Hamood and, Said Boussakta, “Fast Walsh–Hadamard– Fourier transform algorithm,” Trans. Signal Processing, vol. 59, no. 11, pp. 5627-5631, November 2011
Teng Su, and Feng. Yu, “A Family of Fast Hadamard–Fourier Transform Algorithms,” Signal Processing Letters, vol. 19, no. 9, pp. 583-586, September 2012.
Zulfikar and H. Walidainy, "A Novel 4-Point Discrete Fourier Transforms Circuit based on Product of Rademacher Functions," IEEE Proceeding of International Conference of Electrical Engineering and Informatics (ICEEI), pp:142-147, Bali, Indonesia, August 10-11, 2015
Zulfikar, Z. and Walidainy, H., 2016. Design of 8-point DFT based on Rademacher Functions. International Journal of Electrical and Computer Engineering (IJECE), 6(4), pp.1551-1559
M. Y. Zulfikar, S. A. Abbasi, and A. R. M. Alamoud, "FPGA Based Analysis and Multiplication of Digital Signals," Proceedings of IEEE Second International Conference on Advances in Computing, Control, and Telecommunication Technologies (ACT 2010), pp: 32-36, Jakarta, Indonesia, 2010.
M. Y. Zulfikar, S. A. Abbasi, and A. R. M. Alamoud, “FPGA Based Processing of Digital Signals using Walsh Analysis,” Proceeding of IEEE International Conference on Electrical, Control and Computer Engineering (INECCE 2011), pp: 440-444, 21-22 June, Pahang, Malaysia, 2011.
Zulfikar, S. A. Abbasi, and A. R. M. Alamoud, “A Novel Complete Set of Walsh and Inverse Walsh Transforms for Signal Processing,” Proceeding of IEEE International Conference on Communication Systems and Network Technologies (CSNT 2011), pp: 504-509, Katra, Jammu, 3-5 June 2011.
Zulfikar, S. A. Abbasi, and A. R. M. Alamoud, “FPGA Based Complete Set of Walsh and Inverse Walsh Transforms for Signal Processing,” Transaction of Electronics and Electrical Engineering, vol. 18, no. 8, pp. 3-8, October 2012.
Zulfikar, Z., Abbasi, S.A., and Alamoud, A.R.M., 2016. FPGA Hardware Realization: Addition of Two Digital Signals Based on Walsh Transforms. International Journal of Electrical and Computer Engineering (IJECE), 6(6), pp.2688-2697
M. G. Karpovsky, R. S. Stankovic and J. T. Astola, Spectral Logic and Its Applications for The Design of Digital Devices, John Wiley & Sons Inc. Publication, New Jersey, 2008
John. G. Proakis, and Dimitris G. Manolakis, Digital signal processing: principles, algorithms, and applications, 4th ed., Pearson Prentice Hall, New Jersey, 2007.
S. Salivahanan, A. Vallavaraj, and C. Gnanapriya, Digital Signal Processing, McGraw-Hill, New Delhi, 2000.
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