This paper describes a complex multistep problem exercise used in a problem-based learning (PBL) context to introduce the fundamentals of the Fourier transform (FT) and convey the concept of the time domain-frequency domain duality. This complex problem exercise (CPE) consists of obtaining the frequency response (network function) of an RC circuit from voltage measurements taken during the charge/discharge transient and is carried out in circuits, electronics, and electromagnetism laboratories. Although it is widely accepted that undergraduate students should be introduced to FT, this involves substantial and complex mathematics. In order to avoid this difficulty, the discrete Fourier transform (DFT) is used as an approximation to the FT because it is easier to use in a computational environment. The CPE uses a practical approach to concepts such as impulse response, sampling theorem, Nyquist frequency, aliasing, and uncertainty and causality principles; it is thought to be of pedagogical interest as an introduction to the FT. In particular, it could be of interest to instructors and undergraduate students taking courses in circuit theory, electromagnetic theory, linear systems, and digital signal processing in electrical engineering or similar degree programs.