Finite Discrete Convolution
Finite Discrete Convolution with explicit inputs, formulas and domain checks.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Linear discrete convolution, not circular convolution; both sequences start at index0.
Example Calculation
- Sequence a: 1, 2
- Sequence b: 3, 4
[1,2] convolved with[3,4] gives[3,10,8].
Frequently asked questions
How do I use this calculator?
Enter sequence a, sequence b. The result updates automatically. Use Reset to restore the example values.
What method does it use?
c[k]=Σ a[i]b[k−i], using zero outside each finite input sequence.. Linear discrete convolution, not circular convolution; both sequences start at index0.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.