The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.07 - July (2012 vol.61)
pp: 1050-1056
Jianguo Liu , Institute for Pattern Recognition and Artificial Intelligence, Huazhong University of Science and Technology, Wuhan
Chao Pan , Institute for Pattern Recognition and Artificial Intelligence, Huazhong University of Science and Technology, Wuhan
Zhenbing Liu , Guilin University of Electronic Technology, Guilin
ABSTRACT
This paper presents a novel fast algorithm for digital convolutions. It is able to compute arbitrary-length convolutions more efficiently via transforming the convolution into a first-order moment. Although many additions are required, the proposed algorithm has some advantages such as the avoidance of multiplications, simple computation structure, and only integer additions. These advantages contribute to this algorithm being so easy that it can compute convolutions rapidly. Based on the proposed algorithm a very simple and scalable systolic array without multipliers and ROM has been developed leading to more efficient VLSI implementation of convolutions.
INDEX TERMS
Convolution, first-order moment, systolic array.
CITATION
Jianguo Liu, Chao Pan, Zhenbing Liu, "Novel Convolutions Using First-Order Moments", IEEE Transactions on Computers, vol.61, no. 7, pp. 1050-1056, July 2012, doi:10.1109/TC.2011.126
REFERENCES
[1] G.Q. Liu and V. Kreinovich, “Fast Convolution and Fast Fourier Transform under Interval and Fuzzy,” J. Computer and System Sciences, vol. 76, pp. 63-76, 2010.
[2] H.J. Nussbaumer, “Fast Polynomial Transform Algorithms for Digital Convolution,” IEEE Trans. Acoustics, Speech and Signal Processing, vol. ASSP-28, no. 2, pp. 205-215, Apr. 1980.
[3] R.E. Blahut, Fast Algorithms for Digital Signal Processing. Addison-Wesley, 1985.
[4] R.C. Agarwal and J.W. Cooley, “New Algorithms for Digital Convolution,” IEEE Trans. Acoustics, Speech and Signal Processing, vol. ASSP-25, no. 5, pp. 392-410, Oct. 1977.
[5] M.J. Narasimha, “Modified Overlap-Add and Overlap-Save Convolution Algorithms for Real Signals,” IEEE Signal Processing Letters, vol. 13, no. 11, pp. 2777-2788, Nov. 2006.
[6] M.J. Narasimha, “Linear Convolution Using Skew-Cyclic Convolutions,” IEEE Signal Processing Letters, vol. 14, no. 3, pp. 173-176, Mar. 2007.
[7] D.M. Mount, T. Kanungo, N.S. Netanyahu, C. Piatko, R. Silverman, and A.Y. Wu, “Approximating Large Convolutions in Digital Images,” IEEE Trans. Image Processing, vol. 10, no. 12, pp. 1826-1835, Dec. 2001.
[8] D.F. Chiper, M.N.S. Swamy, M.O. Ahmad, and T. Stouraitis, “Systolic Algorithms and a Memory-Based Design Approach for a Unified Architecture for the Computation of DCT/DST/IDCT/IDST,” IEEE Trans. Circuits Systems I: Regular Papers, vol. 52, no. 6, pp. 1125-1137, June 2005.
[9] O. Ersoy, “Semisystolic Array Implementation of Circular, Skew Circular, and Linear Convolutions,” IEEE Trans. Computers, vol. C-34, no. 2, pp. 190-196, Feb. 1985.
[10] C. Cheng and K.K. Parhi, “Hardware Efficient Fast DCT Based on Novel Cyclic Convolution Structures,” IEEE Trans. Signal Processing, vol. 54, no. 11, pp. 4419-4434, Nov. 2006.
[11] P.K. Meher, “Parallel and Pipelined Architectures for Cyclic Convolution by Block Circulant Formulation Using Low-Complexity Short-Length Algorithms,” IEEE Trans. Circuits and Systems for Video Technology, vol. 18, no. 10, pp. 1422-1431, Oct. 2008.
[12] H.C. Chen, J.I. Guo, T.S. Chang, and C.W. Jen, “A Memory-Efficient Realization of Cyclic Convolution and Its Application to Discrete Cosine Transform,” IEEE Trans. Circuits and Systems for Video Technology, vol. 15, no. 3, pp. 445-453, Mar. 2005.
[13] P.K. Meher, “Systolization of DA-Based Calculation of Finite Digital Convolution,” IEEE Trans. Circuits and Systems II, Express Briefs, vol. 53, no. 8, pp. 707-711, Aug. 2006.
[14] F.H.Y. Chan, F.K. Lam, H.F. Li, and J.G. Liu, “An All Adder Systolic Structure for Fast Computation of Moments,” J. Very Large-Scale Integration Signal Processing, vol. 12, no. 2, pp. 159-175, 1996.
[15] J.G. Liu, H.F. Li, F.H.Y. Chan, and F.K. Lam, “A Novel Approach to Fast Discrete Fourier Transform,” J. Parallel and Distributed Computing, vol. 54, pp. 48-58, 1998.
[16] T. Lundy, J. Van Buskirk, W. Ridge, and CO, “A New Matrix Approach to Real FFTs and Convolutions of Length $2^k$ ,” J. Computing, vol. 80, pp. 23-45, 2007.
[17] J. Hee, “Fast Convolution Using Polynomial Transforms,” http:/jenshee.dk, Jan. 2004.
[18] C.N. Marimuthu, D.P. Thangaraj, and A. Ramesan, “Low Power Shift and Add Multiplier Design,” Int'l J. Computer Science and Information Technology, vol 2, pp. 12-22, June 2010.
[19] H.C. Chen, J.I. Guo, C.W. Jen, and T.S. Chang, “Distributed Arithmetic Realisation of Cyclic Convolution and its DFT Application,” IEE Proc.—Circuits, Devices and Systems, vol. 152, no. 6, pp. 615-629, Dec. 2005.
11 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool