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Optimizing Student Learning and Retention of Time- and Frequency- Domain Concepts Through Numerical Computation Projects Steve Warren, Ph.D. Department of Electrical & Computer Engineering, Kansas State University

Abstract

The ability to analyze signals and systems in both the time and frequency domains is an essential outcome in most engineering curricula. However, concepts such as time-domain convolution and frequency-domain spectra can be elusive to students. While most students can learn the mathematical procedures whereby they obtain correct answers on homework and exams, many lack the higher-level understanding that aids long-term retention. This paper addresses the creation of MATLAB and C projects that facilitate learning in these areas by clearly stating learning objectives, maintaining student interest with real-world applications, partitioning large projects into incremental modules, and providing the repetition necessary for long-term retention. The underlying assumptions for this work are two-fold: (1) if a student can write the numerical software to solve a problem, they understand the theoretical principles well and (2) students receive personal satisfaction and gain confidence when their software produces correct results. The illustrative time-domain projects described here address linear convolution and trigonometric/exponential Fourier series. The frequency-domain projects address the computation of discrete Fourier transforms, spectral assessment, and time-frequency analysis. Real-world applications such as filter cascades for signal conditioning, tone control knobs for audio systems, and parameter extraction from biomedical signals drive these multi-week efforts. Typically assigned in the junior and senior years of the undergraduate curriculum, these efforts are precursors to upper-level undergraduate and graduate projects that incorporate full user interfaces. Through end-of-year evaluations and post-graduate feedback, many students refer to these projects as the highlight of their course experience.

Introduction

Linear systems (a.k.a., signals and systems) courses typically address both time- and frequency- domain principles. Continuous and sampled signals are important in both domains. While linear superposition and signal characteristics (e.g., behavior and symmetry) are conceptually straightforward for students, convolution is an elusive concept. Although it may have already been introduced in a previous circuit theory course, it was most likely presented as a flip-and- shift, or fold-and-slide, approach that represents the mathematics but is not physically intuitive. Additionally, while the Fourier series approach to building arbitrary signals with sinusoids makes sense to students, the mathematics involved with calculating the Fourier coefficients can be difficult for the average student. Students may also learn about Laplace transforms and filter transfer functions in an earlier circuit theory course. While they can demonstrate frequency- dependent behavior with analog circuits in the laboratory, they find it difficult to (a) conceptually map time-domain signal character to frequency-domain spectra and (b) describe the effect of a frequency-domain filter on the shape of a time-domain signal, even if they understand the

Proceedings of the 2005 American Society for Engineering Education Annual Conference and Exposition Copyright ©2005, American Society for Engineering Education

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Warren, S. (2005, June), Optimizing Student Learning And Retention Of Time And Frequency Domain Concepts Through Numerical Computation Projects Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--14954