Convolução como um apelo da natureza

In this manuscript, we show in an educational way, how the operation known as convolution works. This is an important subject as it has a relevant physical appeal. At first, we will discuss the sampling concept where we will briefly focus on the decomposition of signals through a function known as impulse function. We address the impulse function and talk about the peculiarities of its representation in the discrete domain. We then talk about time signal shifts and address some very simple algorithms that deal with the pure convolution problem, without noise and without filters, in an elementary focus. We will deep-dive into the concept with the convolution integral culminating to the discussion with the Toeplitz matrix which is a key component of discrete convolution. It is worth mentioning that the methodology used in this work is simple and may offer the possibility to test a linear physical system for any input, a subject that is little treated in current literature. Finally, we conclude with some notes on the famous operation which has been used a long time for testing linear and time invariant physical systems, as it is very important in real applications in signals, telecommunication and image processing.