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This paper presents an introductory signal processing laboratory and examines this laboratory exercise in the context of problem-based learning (PBL). Centered in a real-world application, a cochlear implant, the exercise challenged students to demonstrate a working software-based signal processor. Partnering in groups of two or three, second-year electrical and computer engineering and biomedical engineering students used MATLAB graphical user interface programs, complemented with their own original MATLAB code, to design filters suitable for achieving a filter bank decomposition of an audio signal. Rather than using the envelope-detected output for direct electrical stimulation of auditory nerve fibers as in an implant, the students reconstructed the signal by modulating sinusoids to yield an acoustic simulation. To appreciate the impact of filter order on sound intelligibility, students were asked to reconstruct signals using 4-16 filter channels for both speech and music and to examine the results critically. The lab served as a substrate upon which to solidify fundamental signal processing concepts such as the distinction between time and frequency domains, constructing and interpreting spectrograms, sampling, spectral decomposition, filtering, and reconstruction. In the spirit of PBL, the students examined engineering tradeoffs and discussed implementations when they were asked to consider realizing a significantly higher channel count (128-channel) device. To determine how the laboratory exercise impacted student learning and comprehension, as well as the level of student engagement achieved with this compelling application, an anonymous online survey was administered at the end of the course. The survey outcomes, as well as the components of the lab, are discussed in the context of PBL pedagogy.