Digital Signal Processing. Applications to Communications by Salvatore D. Morgera

By Salvatore D. Morgera

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5 ] C. M. Fiduccia, On Obtaining Upper Bounds on the Complexity of Matrix Multiplication, Plenum Press, New York, 1972. 6 ] V. Strassen, Evaluation of Rational Functions, Plenum Press, New York, 1972. 5. 7 ] D. Dobkin, "On the Arithmetic Complexity of a Class of Com­ putations," Thesis in the Division of Engineering and Applied Physics, Harvard University, Cambridge, MA, Sept. 1973. 8 ] A. Lempel and S. Winograd, "A New Approach to Error-Correcting Codes," IEEE Trans. Inform. Theory, vol. IT-23, pp.

Of Mults. 0794 54 CHAPTER 3. 4: Complexity of Cyclic Convolution of Some Factor Lengths Over a Field of Constants GF{Z). Length ΛΓ No. 1. 5: Complexity of Cyclic Convolution Algorithm Over a Field of Constants GF(4). Length N 15 63 255 4095 No. of Mults. 1. Just a fac­ tor of two increase in field size is seen to substantially decrease (by approximately 30%) the multiplicative complexity; however, computa­ tion of the linear forms associated with the matrices A, B, and C whose elements are now over the enlarged field is somewhat more complex.

Winograd, "A New Approach to Error-Correcting Codes," IEEE Trans. Inform. Theory, vol. IT-23, pp. 503-508, July 1977. 9 ] R. W. Brockett and D. Dobkin, "On the Optimal Evaluation of a Set of Bilinear Forms," in Proc. Fifth Ann. ACM Symp. on Theory of Computing, Austin, Texas, pp. 88-95, April-May 1973. 10 ] F. J. MacWilliams and N. J. A. Sloane, The Theory of ErrorCorrecting Codes, North Holland, 1977. Chapter 3 Efficient Finite Field Algorithms The discrete convolution of sequences plays an important role in signal processing.

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