Second, we begin with rudimentary, oft-repeated motifs, which we then perturb and embellish to create more elaborate systems. We prefer to invoke elementary geometry, algebra, and trigonometry before college mathematics. First, we recast certain advanced concepts in a vernacular that's accessible even to recent high school graduates. This exposes students to refined engineering techniques and interesting applications early. 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 im- mediately after the convolution sum and well before the full- scale infrastructure of Fourier analysis.
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