Convolve a 5-sample boxcar with a 4-tap moving average in the sandbox, and predict every output sample before you read it off the screen.
Convolution is the one operation the rest of DSP is built on. If you can flip, shift, multiply and sum by hand, filtering, correlation and the FFT all become the same move.
Open the sandbox and set the two sequences to these exact values. They are the demo's opening state, so a Reset gets you here too.
x = [1, 1, 1, 1, 1]
h = [0.25, 0.25, 0.25, 0.25]
Then drag the lag control n from left to right and watch the arithmetic line under panel 1.
Set n to 0. Only one tap of h overlaps x. Predict y[0], then read it.
Panel 2 shows y[0] = 0.25 — the single product x[0]·h[0] = 1·0.25.
Move n to 3. Now all four taps of h sit on ones. Predict y[3], then read it.
Panel 2 shows y[3] = 1 — four taps of 0.25 each land on a 1, so the sum is full overlap.
Drag n to the end. Predict how many samples y has, then read the length readout.
The output is 8 samples long: len(x) + len(h) - 1 = 5 + 4 - 1 = 8.
Everything above is waiting in the sandbox. Build your own x and h, then step the lag and watch where every number comes from.
- Read y[0] = 0.25 off a single overlapping product
- Found the peak y[3] = 1 at full overlap
- Confirmed the length law len(x)+len(h)-1 = 8
- Every value you predicted is the demo's own arithmetic, not a picture