Unified Vector Multiplication Approach for Calculating Convolution and Correlation


  •   Innocent E. Okoloko


This paper is a theoretical analysis of discrete time convolution and correlation and to introduce a unified vector multiplication approach for calculating discrete convolution and correlation, both of which are important concepts in the design and analysis of signals and systems and are usually encountered in the first course in signals and systems analysis. There are software tools for calculating them, however, it is important to learn now to compute them by hand. Several methods have been proposed to compute them by hand, most of which can be very involving. However, a closer look at the concepts reveal that the convolution and correlation sums are actually vector multiplication with diagonalwise addition and for finite sequences, can be computed by hand the same way. The method is also extended to N-point circular convolution. The method also makes it clearer to see the similarities and differences between convolution and correlation.

Keywords: Convolution, correlation, N-point circular convolution, vector multiplication


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.


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How to Cite
Okoloko, I.E. 2021. Unified Vector Multiplication Approach for Calculating Convolution and Correlation. European Journal of Engineering and Technology Research. 6, 4 (Jun. 2021), 129-134. DOI:https://doi.org/10.24018/ejers.2021.6.4.2488.