Discrete Time Convolution is Multiplication without Carry


  •   Innocent E. Okoloko


In this paper an analysis of discrete-time convolution is performed to prove that the convolution sum is polynomial multiplication without carry, whether the sequences are finite or not, by using several examples to compare the results computed using the existing approaches to the polynomial multiplication approach presented here. In the design and analysis of signals and systems the concept of convolution is very important. While software tools are available for calculating convolution, for proper understanding it is important to learn now to calculate it by hand. To this end, several popular methods are available. The idea that the convolution sum is indeed polynomial multiplication without carry is demonstrated in this paper. The concept is further extended to deconvolution, N-point circular convolution and the Z-transform approach.

Keywords: Convolution, deconvolution, N-point circular convolution, Z-transform


B. P. Lathi, Linear Systems and Signals. Carmichael, CA: Berkeley-Cambridge, 1998.

S. S. Soliman and M. D. Srinath, Continuous and Discrete Signals and Systems. Englewood Cliffs, NJ: Prentice-Hall, 1990.

R. D. Strum and D. E. Kirk, First Principles of Discrete Systems and Digital Signal Processing. Reading, MA: Addison-Wesley, 1988.

J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithm, and Applications, 4th ed. Upper Saddle River, NJ: Prentice-Hall, 2007.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 3rd ed. Upper Saddle River, NJ: Prentice-Hall, 2014.

A. V. Oppenheim, A. S. Willsky and S. H. Nawab, Signals and Systems, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1997.

J. W. Pierre, “A Novel Method for Calculating the Convolution Sum of Two Finite Length Sequences,” IEEE Trans. Education, vol. 39, no. 1, pp. 77–80, Feb. 1996.

I. E. Okoloko, “Unified Vector Multiplication Approach for Calculating Convolution and Correlation,” European Journal of Engineering and Technology Research, vol. 6, no. 4, pp. 129–134, Jun. 2021.


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How to Cite
Okoloko, I.E. 2021. Discrete Time Convolution is Multiplication without Carry. European Journal of Electrical Engineering and Computer Science. 5, 5 (Oct. 2021), 64–68. DOI:https://doi.org/10.24018/ejece.2021.5.5.358.