Convolution is a typical operation in signal processing that expresses how two functions modify each other and create a third function. Convolution layers are actually implementing an autocorrelation operation, but in practice for our case convolution and autocorrelation are the same, as they can be interchanged with a simple rotation operation.
Let's call our input x, the set of weights it passes through w, the output signal s, and the time t. We want to give more importance to inputs that are more recent, therefore we will use the function w(a) to define the weights, where a is the age of the measurement. The convolutional operation is the process of combining the signal s and the set of weights, which is also called a kernel. As we are dealing with data from real applications and not just match abstractions, the time must be discrete. In mathematical...