June 12, 2005
June 12, 2005
June 15, 2005
10.180.1 - 10.180.12
An Innovative Software Tool for Teaching Discrete Convolution from the Perspective of the Output Signal in Digital Signal Processing: Its Software Design and Implementation, and Usage in Teaching and Learning S. Easwaran Department of Computer Sciences and Computer Engineering Xavier University of Louisiana
This paper describes an approach and a novel software tool that was developed and used by the author of this paper to visually teach discrete convolution to students encountering it for the first time. In order to accomplish this to aid understanding of concepts without losing rigor or completeness, two novel software tools each viewing discrete convolution from a different perspective were designed and implemented in Microsoft Visual C++. This paper describes one of these two software tools. The other is described in a companion paper1. The software tool described in this paper was designed and implemented to visually teach discrete convolution by interpreting the discrete convolution equation from the perspective of the output signal in Linear Shift-Invariant systems. By using the approach and software tool described in this paper, it was possible to visually teach discrete convolution from the perspective of the output signal very clearly and thoroughly in a shorter time than was otherwise possible.
Discrete (or digital) convolution is a fundamental operation and concept that is used extensively in the field of Digital Signal Processing (DSP). It is the basis of many DSP techniques, and it provides a mathematical framework for DSP3-8. However, it is also one of the most difficult techniques to understand and implement especially for those encountering it for the first time7.
In order to provide a complete and proper understanding of this fundamental concept to students encountering it for the first time, a systematic approach of teaching this concept and topic was adapted and developed from various sources by the author3-8. The approach used was by first providing discrete convolution as a mathematical operation. It was then interpreted and explained as an input-output relationship for Linear Shift-Invariant (LSI) systems. Based on this, discrete convolution was explained as an operation that can be interpreted from two different perspectives of LSI systems – namely, from the perspective of the input signal, or from the perspective of the output signal.
Further, in order to visually teach these interpretations to aid understanding of concepts without losing rigor or completeness, two novel software tools each viewing discrete convolution from a different perspective were designed and implemented in Microsoft Visual C++ by the author of
"Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education"
Easwaran, S. (2005, June), An Innovative Software Tool For Teaching Discrete Convolution From The Perspective Of The Output Signal In Digital Signal Processing: Its Software Design And Implementation, And Usage In Teaching And Learning 2 Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--14352
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