How this calculator works
Treat both finite inputs as zero outside their listed indices. Multiply every sample pair and accumulate each product at the sum of its two indices. This produces the full linear convolution with length M + N - 1. It is useful for finite impulse responses, coefficient multiplication and discrete probability sums when the inputs have those interpretations.
Formula
y[n] = Σₖ x[k]h[n-k], with x and h zero outside their supplied ranges. Output length = M + N - 1.
Worked example
For [1, 2] convolved with [3, 4], y[0] = 1 × 3 = 3, y[1] = 1 × 4 + 2 × 3 = 10, and y[2] = 2 × 4 = 8.
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Frequently asked questions
Is this circular convolution?
No. It is full linear convolution without wrapping. Circular convolution requires a chosen period.
Do the sequences need equal lengths?
No. Each input can have its own length, from one to one hundred samples.
Where does indexing start?
The first listed sample is index zero in each input. If your data start at other indices, add those two starting indices to the output labels.