Discrete convolution is a fundamental operation in signal processing. It describes how the shape of one signal is modified by the shape of another. It's used in filtering, audio processing, image analysis, and more.

The Formula:

The convolution of two signals, $x[n]$ and $h[n]$, is denoted by $(x * h)[n]$ and is calculated as:

$$ y[n] = (x * h)[n] = \sum_{k=-\infty}^{\infty} x[k]h[n-k] $$

For finite signals starting at index 0, this simplifies. The resulting signal $y[n]$ will have a length of $length(x) + length(h) - 1$.

How to Use:

• Enter your signals as comma-separated numbers (e.g., 1, 2, 3).
• The calculator will compute the resulting signal $y[n]$ and show the steps involved.