## Signal processing

In signal processing, zero padding refers to the practice of adding zeroes to a time-domain signal. Zero-padding is often done before performing a fast Fourier transform on the time-domain signal.

## Neural networks

In convolutional neural networks, zero-padding refers to surrounding a matrix with zeroes. This can help preserve features that exist at the edges of the original matrix and control the size of the output feature map.

Below is an example of a padding operator \(\mathrm{Pad}(n, \mathbf X)\) that adds \(n\) layers of zeroes around the matrix \(\mathbf X\). \[ \mathbf X = \begin{bmatrix} a & b & c \\ d & f & g \\ h & j & k \end{bmatrix}, \] \[ \mathrm{Pad}(1, \mathbf X) = \begin{bmatrix} 0 & 0 & 0 & 0 & 0 \\ 0 & a & b & c & 0 \\ 0 & d & f & g & 0 \\ 0 & h & j & k & 0 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix} \]