Calculate the convolution of two comma-separated signals and view the resulting sequence with step-by-step summation details for each output.
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Signal Convolution Formula
For two finite discrete signals, the calculator uses linear convolution:
y[n] = Σₘ₌₀⁽M - 1) x[m] × h[n - m]
- x[m] = first input signal
- h[n-m] = shifted value from the second input signal
- y[n] = convolution output at index n
- M = length of the first signal
- n = output index
The calculator treats values outside the entered signal lengths as zero. If signal 1 has length M and signal 2 has length N, the convolution result has this length:
L = M + N - 1
- L = number of values in the convolution result
- M = number of values in signal 1
- N = number of values in signal 2
Enter signals as comma-separated numbers, such as 1,2,3. The first output value is indexed as y[0].
Convolution Result Length and Input Format
| Signal 1 length | Signal 2 length | Result length |
|---|---|---|
| 3 | 3 | 5 |
| 4 | 2 | 5 |
| 5 | 4 | 8 |
Common Signal Convolution Checks
| Input | Meaning | Expected behavior |
|---|---|---|
| 1,0,0 | Unit impulse at the first index | Returns the other signal, with added trailing zeros if needed |
| 0,1,0 | Delayed impulse | Shifts the other signal by one index |
| Negative values | Signed signal samples | Products and sums keep their signs |
Example
If signal 1 is 1,2,3 and signal 2 is 4,5, the result has length 3 + 2 - 1 = 4.
The convolution is:
[4, 13, 22, 15]
This comes from multiplying overlapping values as one signal slides across the other.
