Calculator Inputs
Enter comma-separated values. Spaces and new lines also work.
Example Data Table
This worked example uses full linear convolution with x[n] = [1, 2, 1] and h[n] = [1, -1, 2].
| Sequence / Index | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| x[n] | 1 | 2 | 1 | — | — |
| h[n] | 1 | -1 | 2 | — | — |
| y[n] = x[n] * h[n] | 1 | 1 | 1 | 3 | 2 |
Formula Used
Discrete linear convolution:
y[n] = Σ x[k] · h[n - k]
For finite sequences, the full output length equals N + M - 1, where N is the length of x[n] and M is the length of h[n].
When start indices are provided, the first full-output index becomes nstart = xstart + hstart.
In circular mode, the calculator wraps products into a fixed period L using circular indexing:
yc[n] = Σ x[k] · h[(n - k) mod L]
Optional scaling and normalization are applied after the selected convolution result is produced.
How to Use This Calculator
- Enter the first discrete signal in the x[n] field.
- Enter the second discrete signal in the h[n] field.
- Set the starting index for each sequence if samples begin elsewhere.
- Choose Full, Same, Valid, or Circular mode.
- For circular mode, enter the desired wrap length L.
- Adjust scale factor, decimal places, sample period, and normalization if needed.
- Press Calculate Convolution to show results above the form.
- Download CSV or PDF files when you need shareable output.
Frequently Asked Questions
1. What does convolution measure in discrete signals?
It measures how one sequence overlaps another while one is shifted and multiplied sample by sample. The summed products form the output sequence.
2. Why do start indices matter?
Start indices determine where each sample exists on the number line. They shift the output index range without changing sample magnitudes.
3. What is the difference between full, same, and valid modes?
Full returns every overlap position. Same keeps the output aligned to x[n]. Valid keeps only positions with complete overlap, avoiding zero-padding effects.
4. When should circular convolution be used?
Use circular convolution for periodic signals, discrete Fourier methods, block processing, or systems that wrap indices within a fixed sequence length.
5. Can this calculator handle decimals and negative numbers?
Yes. The parser accepts signed and decimal values, so the calculator is suitable for practical signal-processing exercises and engineering-style datasets.
6. What does normalization do?
Normalization rescales the computed output. It can divide by the largest absolute value or by the sum of absolute values for easier comparison.
7. Why is the output length N + M - 1?
That length counts every shift where at least one pair of samples overlaps. It is the standard size of full linear convolution.
8. Can I export the computed results?
Yes. The calculator provides CSV export for spreadsheets and PDF export for reports, assignments, lab notes, or project documentation.