Rethinking Fourier's Legacy in Signals and Systems Education

In our gateway Signals and Systems courses at UC Berkeley we teach design-oriented modeling and analysis of linear, time-invariant systems in the frequency domain immediately after the convolution sum and well before the full-scale infrastructure of Fourier analysis. This exposes students to refined engineering techniques and interesting applications early. Two features are integral to our approach. First, we recast certain advanced concepts in a vernacular that's accessible even to recent high school graduates. We prefer to invoke elementary geometry, algebra, and trigonometry before college mathematics. Second, we begin with rudimentary, oft-repeated motifs, which we then perturb and embellish to create more elaborate systems. Throughout, we keep the students mindful of how certain design, modeling, and analytical tools enable a graceful progression from the simple to the more complex structures.