Calculate the convolution of two comma-separated signals and view the resulting sequence with step-by-step summation details for each output.

Enter up to 64 real samples (1,000 characters) per signal, separated by commas. Both sequences begin at index 0; values outside them are zero.

Example: 1, 2, 3. Signed decimals and scientific notation are accepted.

Related Calculators

Signal Convolution Formula

For two finite discrete signals, the calculator uses linear convolution:

y[n] = Σₘ₌₀M - 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 up to 64 real samples per signal as comma-separated numbers, such as 1,2,3. Signed decimals and scientific notation are accepted; empty entries are rejected. Both inputs start at index 0, so the first output is y[0]. This is discrete linear convolution, without a continuous-time sample-interval multiplier or circular wrapping.

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.