Even if we work only with finite and discrete convolutions, it's useful to start providing the standard definition based on integrable functions. For simplicity, let's suppose that f(τ) and k(τ) are two real functions of a single variable defined in ℜ. The convolution of f(τ) and k(τ) (conventionally denoted as f ∗ k), which we are going to call kernel, is defined as follows:
The expression may not be very easy to understand without a mathematical background, but it can become exceptionally simple with a few considerations. First of all, the integral sums over all values of τ; therefore, the convolution is a function of the remaining ...
