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Teaching Signals and Systems through Visualization with Image Processing Richard R. Schultz University of North Dakota

Abstract: Most signals and systems courses teach abstract concepts such as convolution and Fourier transform theory using only one-dimensional (1-D) signals. However, real-life 1-D signals such as speech and music do not possess easily recognizable visual forms, and thus the effect of applying a particular signal processing technique to the data is difficult to visualize. Applying various algorithms to 2-D image data, on the other hand, results in obvious visual changes when the input and output images are compared side-by-side. This paper describes a set of image processing experiments which can help students comprehend many important systems-related concepts, including spatial convolution, space-frequency duality, image compression, spatial and contrast enhancement, degradation due to noise, and image restoration. By viewing the results of a particular image processing algorithm, an intuitive understanding of the corresponding 1-D signal processing concept is acquired.

1. Introduction It has been said that a single picture is worth a thousand words. Digital image processing is becoming an integral part of science and engineering for this very reason: visualization aids immensely in the understanding of large data sets. Furthermore, an intuitive understanding of abstract systems-related topics such as convolution and Fourier transform theory can be acquired when these algorithms are applied to images. Often, these concepts are taught to electrical engineering students in a signals and systems course which deals exclusively with 1-D signals. However, the data smoothing effect of a lowpass filter can be better visualized by comparing an input image to the corresponding blurry filtered image. Similarly, seeing the edges detected by a 2-D highpass filter applied to an image is a far more dramatic visual effect than that provided by the corresponding 1-D filter applied to a speech signal. Once a systems concept has been made intuitively clear, understanding the mathematical definitions and explanations should become easier for the students. A set of laboratory exercises have been developed for a course in digital image processing which will aid in teaching systems-related concepts such as spatial convolution, space-frequency duality, image compression, spatial and contrast enhancement, signal degradation due to noise, and image restoration. All laboratory exercises were originally implemented using the C programming language on a UNIX computer system. Students in a digital image processing course taught by the author during the fall semester of 1996 were provided with source code templates of a number of useful image processing algorithms. These C source code templates were deliberately missing critical components

This work was supported in part by the National Science Foundation Faculty Early Career Development (CAREER) Program, grant number MIP-9624849. In addition, this material is based upon work supported in part by the U.S. Army Research Office under contract number DAAH04-96-1-0449.

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Schultz, R. R. (1997, June), Teaching Signals And Systems Through Visualization With Image Processing Paper presented at 1997 Annual Conference, Milwaukee, Wisconsin. 10.18260/1-2--6820