Convolution Integral: How a Graphical Type of Solution Can Help Minimize Misconceptions

Hendra J. Tarigan

doi:10.33021/jeee.v3i2.1489

Authors

Hendra J. Tarigan President University

DOI:

https://doi.org/10.33021/jeee.v3i2.1489

Abstract

A physical system, Low Pass Filter (LPF) RC Circuit, which serves as an impulse response and a square wave input signal are utilized to derive the continuous time convolution (convolution integrals). How to set up the limits of integration correctly and how the excitation source convolves with the impulse response are explained using a graphical type of solution. This in turn, help minimize the students' misconceptions about the convolution integral. Further, the effect of varying the circuit elements on the shape of the convolution output plot is presented allowing students to see the connection between a convolution integral and a physical system. PSpice simulation and experiment results are incorporated and are compared with those of the analytical solution associated with the convolution integral.

Author Biography

Hendra J. Tarigan, President University

1Study Program of Electrical Engineering

References

B.P. Lathi and R. Green, “Time-domain Analysis of Continuous-time System,” in Linear Systems and Signals, 3rd ed. (Oxford, New York, NY 10016), Chap. 2, p. 180.

I.S. Goldberg, M.G. Block and R.E. Rojas, “A Systematic Method for the Analytical Evaluation of Convolution Integrals,” IEEE Transactions on Education (2002), vol. 45, pp. 65-69.[3] M. Souare, V. Chankong, and C. Papachristou. “Undergraduate Notes on Convolutions and Integration by Parts,” ASEE 2014 Zone Conference, University of Bridgeport, Bridgeport, CT, USA (2014), pp.??[4] R. Nasr, S.R. Hall, and P. Garik, “Student Misconceptions in Signals and Systems and their Origins—Part II,” 35th ASEE/IEEE Frontiers in Education Conference, Indianapolis, IN, USA (2002), pp. TAE 26-31.

J.K. Nelson and M.A. Hjalmarson, “Students' Understanding of Convolutions,” IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, BC, Canada (2013), pp. 4339-4343.

R. Togneri and S. Male, “Signals and Systems: Casting It as an Action-Adventure Rather Than a Horror Genre,” IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK (2019), pp. 7859-7863.

A.V. Oppenheim, A.S. Willsky and S.H. Nawab “Continuous-Time LTI Systems: The Convolution Integral,” in Signals and Systems, 2nd ed. (Prentice Hall, New Jersey 07458, 1993), pp.90-103.

J.W. Nilsson and S.A. Riedel, “The Laplace Transform in Circuit Analysis,” in Electric Circuits, 10th