System Properties Explorer

Concept notes

This applet serves as a conceptual simulator to help students diagnose system properties intuitively and formally.

• Causality Visualization: When sliding $t_0$, any dependency mapping to $\tau > t_0$ crosses into the visually red "Future" region, explicitly showing causality violations.
• BIBO Stability Test: Toggling the test signal applies the unit step $u(t)$ (a strictly bounded signal). Students can visually observe if the output $y(t)$ grows unbounded (e.g., in the Accumulator or Time-Varying Gain presets).
• Time Invariance: Students can use the $t_0$ slider to shift the observation window. For Time-Varying Gain ($t \cdot f(t)$), sliding $t_0$ changes the amplitude of the mapped signal, visually demonstrating shift-variance.
• Linearity Misconception: The $f(t)+2$ preset proves that $y=mx+b$ logic fails for linear systems (requires zero-in, zero-out).
• Predictive Pedagogy: Forced choice ("Predict Yes/No") requires cognitive commitment before revealing the answer, improving retention over passive reading.