Convolution

Here, a signal (grey) is convolved with a gaussian kernel (red), meaning we “slide” the kernel across the signal, computing each output value (green) by multiplying the kernel with the underlying signal (blue).

Long Kernel

In this first example, we will examine convolution using a long kernel.

Short Kernel

Next, we can examine how things are different when we use a shorter kernel.

Technical Notes

Some technical notes on the convolution:

• The “multiplication” applied between the kernel and the signal is the dot product
• Only the range where the kernel fully overlaps the signal is shown
• By definition, convolution applies the reverse of the kernel
  • In these examples, the kernel is symmetric, so it doesn’t change anything