Signal processing using vector space methods: An introspective

In this paper, we observe that an education that ends with a conventional transform-oriented course in signal processing leaves students inadequately prepared to engage with the research literature. A course built upon vector space methods, as we describe, provides an introduction to a broad range of applied mathematics topics that will prepare students to work on a variety of signals related problems. Such a course has been taught at Utah State University for over ten years. We describe the course in some detail, and provide some introspection on lessons learned.