Examples
Examples
Try the starting example
- First finite real sequence
- 1,2
- Second finite real sequence
- 3,4
- Output mode: full, same or valid
- full
- Convolved sequence
- 3, 10, 8
- Output length
- 3
- Starting index relative to full convolution
- 0
- Sum of returned sequence
- 21
Try another scenario
- First finite real sequence
- 1,2
- Second finite real sequence
- 3,4
- Output mode: full, same or valid
- valid
- Convolved sequence
- 10
- Output length
- 1
- Starting index relative to full convolution
- 1
- Sum of returned sequence
- 10
Calculation method
Calculation method
Convolved sequence
Full y[k]=sum(a[i]×b[k−i]) with zero outside input bounds. Same takes the centred max(input lengths) entries; valid keeps entries with complete overlap.
Output length
Number of returned entries.
Starting index relative to full convolution
Full starts at 0; same at floor((full length−max input length)/2); valid at min input length−1.
Sum of returned sequence
Sum only the selected output entries; truncated modes do not preserve the full-convolution sum identity.
Symbols and units
- a
- First finite real sequence
- b
- Second finite real sequence
- c
- Output mode: full, same or valid
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
sum(list) adds all entries in the list.
Assumptions & limits
Assumptions & limits
- Linear discrete convolution of two finite real sequences, with combined input length at most 500. This is not circular convolution; full indexing assumes both input first elements have index zero. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
NumPy: linear convolution modes ↗
Background reading; this does not imply endorsement or independent review of SumFizz.