Design a discrete filter and apply it to a noisy signal.
Build a digital-filter tool: design an IIR filter, examine its frequency response, and apply it to clean a noisy signal — the practical payoff of the z-transform.
Design a Butterworth low-pass with scipy.signal.butter for a given cutoff and sample rate, plot its freqz response, and filter a noisy test signal — confirming the noise band is attenuated.