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SIGNALS / FINITE CONVOLUTION

See every term
in the sum.

Edit a short input and a short kernel. Follow how each output is built from shifted products, including the zeros at the boundaries.

y[n] = Σk x[k] h[n − k]Each list starts at index 0 and is zero elsewhere. Keep the full N + M − 1 output.

Choose two sequences

1–24 decimal numbers per list, from −100 to 100, with up to four decimal places. Use commas or spaces. A minus sign is written as -. Results update as you edit.

The complete output

Input length N
Kernel length M
Output entries
Output indices
Input x[k]
Kernel h[j]
Full output y[n]

Dots are samples; stems show signed values. Each plot labels its own vertical scale. Long sequences scroll inside the plot.

Build one output at a time

At this n, align x[k] with h[n−k]. As k increases, the kernel index decreases. The dashed kernel below is shifted and reversed; it is zero outside its list.

x[k]h[n−k] · dashed stems

Scroll the table sideways to read every product. With the table focused, use the left and right arrow keys.

kx[k]n−kh[n−k]Product
Sum

Why a matching-index dot product is different

Convolution pairs x[k] with h[n−k]. For real lists, the separately defined zero-lag correlation r[0] pairs x[k] with h[k]. For x = [1, 2] and h = [3, 4], convolution gives y[0] = 3, while r[0] = 11. Always state the index convention.

KEEP EXPLORING

Take the twelve-question lesson

  1. Download the lesson JSON.
  2. Open RecallWeave and choose it under Bring your own lesson.
  3. Inspect the preview, then select Start this deck.

The lesson uses RecallWeave's existing review and practice. The calculation download keeps your numerical example and every product; it is not a learner record.

Model, source, and attribution

This lab uses finite real lists and full zero-extended linear convolution. It does not wrap indices, crop the result, simulate a continuous signal, or process a recording. Decimal input has four-place precision; output is displayed to at most eight places. All examples are authored teaching inputs.

Read MIT's convolution lecture or the finite-filter notes. The worked course guide accompanies this page.