Final answer:
To compute the convolution of x(t) and v(t), represented as x(t) × v(t), the integral of x(a) multiplied by v(t - a) over all possible values of a is used.
Step-by-step explanation:
The convolution of two functions x(t) and v(t), represented as x(t) × v(t), is a mathematical operation that produces a third function. This function represents the amount of overlap between x(t) shifted by t and v(t) as a function of the shifting. To compute the convolution of two functions, you use the integral:
∑ x(a) · v(t - a) da, over all a from -∞ to ∞.
The convolution integral can be interpreted as the area under the curve of x(a) times v(t-a) as a shifts over all possible values. However, in the practical computation of convolution, the limits of integration are often confined to the domain where the two functions are non-zero.