Signals & Systems Lab

Convolution, step by step

Pick two signals, slide one across the other, and watch the overlap turn into an output — one sample at a time.

Convolution combines two signals into a third one that describes how the shape of one modifies the other — it's the operation underneath filtering, blurring, and how an LTI system responds to any input.

y[n] = Σk x[k] · h[n − k]

To compute one output value y[n]: flip the second signal h in time, slide it so it's centered at n, multiply it point-by-point against x, and add up everything that overlaps. Move the slider below and each of those four steps — flip, shift, multiply, sum — happens once per tick, building the output graph one point at a time.

Signal A — x[k]
Signal B — h[k]
shift n = -12
Overlap — x[k] and h[n−k] (flipped & shifted) k axis
Output — y[n] = Σ x[k]·h[n−k] n axis
y[-12] = 0 (no overlap yet)
x[k] — Signal A, fixed in place h[n−k] — Signal B, flipped & slid to n product / output — what gets summed into y[n]