Convolution of Battery Impulse Response with Motor Load

Overview

This animation visualizes the convolution of an exponential decay (battery impulse response) with a rectangular pulse (motor load). The top coordinate plane shows the two functions and their overlapping area, while the bottom plane plots the resulting transient voltage drop over time.

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Phases

#	Phase Name	Duration	Description
1	Setup	~3s	Create two stacked coordinate planes, label them, and draw the exponential decay curve and rectangular pulse on the top plane.
2	Flip Pulse	~2s	Animate a horizontal flip of the rectangular pulse about the y‑axis to obtain the time‑reversed version.
3	Sliding Convolution	~12s	Move the flipped pulse smoothly from left to right across the exponential curve. Continuously fill the overlapping region with semi‑transparent red.
4	Result Plot	~8s	Simultaneously draw the bottom‑plane curve that records the red area’s integral (the convolution value) as a function of the sliding offset.
5	Outro	~2s	Hold the final state briefly, then fade out both planes.

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Layout

┌─────────────────────────────────────────────┐
│                 TOP PLANE                  │
│   Mechanical Load & Battery Impulse         │
│   (exponential decay + rectangular pulse)   │
├─────────────────────────────────────────────┤
│                BOTTOM PLANE                │
│   Resulting Transient Voltage Drop          │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top Plane	Exponential decay curve $f(t)=e^{-t}$ (for $t\ge0$) and a rectangular pulse $g(t)=\begin{cases}1,&0\le t\le T\\0,&\ ext{otherwise}\end{cases}$. The flipped pulse $g(-t)$ slides horizontally; overlapping region is filled red.	Primary visual of convolution process.
Bottom Plane	Continuous curve $h(\ au)=\int_{-\infty}^{\infty} f(t)\\,g(\ au-t)\\,dt$ plotted in real time as the slide progresses.	Shows the resulting transient voltage drop.
Caption (optional)	Labels for each plane as given above.	Persistent titles at the top of each zone.

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Notes

• Assumptions: Exponential decay parameter set to 1 for simplicity; pulse width $T=2$ units. Total slide distance chosen so the pulse fully traverses the region where the exponential is non‑negligible.
• The red overlapping area is rendered with opacity ≈0.4 to keep underlying curves visible.
• The bottom‑plane curve is drawn incrementally, matching the current overlap value at each frame.
• All animations are paced to keep the total runtime under 30 seconds.
• No additional text is displayed beyond the plane titles.