We address two problems associated with the traditional approach to teaching a junior level course in signals and systems. First, students are expected to develop a facility with a variety of transforms and we have observed that this overwhelms many, reducing them to simply memorizing equations. Second, the usual treatment of Dirac's delta as a function not only leads to serious contradictions with the standard calculus, but also leaves intractable schisms surrounding the transforms of important harmonic functions. We present a unified and consistent approach designed to ameliorate these problems using abstract linear algebra and distribution theory. The approach was implemented for four semesters and exit surveys were conducted to assess pedagogical effectiveness.
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