Question

The rectangle and triangle function were carefully defined so that they satisfy the relationship, rect(t)rect(t) = tri(t). That is, if you convolve a rectangle with itself you get a triangle. Given this relationship, what would be the result of rect(t - 1) *rect(t - 2)?

Answer 1

Convolving shifted rectangle functions rect(t - 1) and rect(t - 2) results in a triangle function tri(t - 3), based on the given relationship that the convolution of rect(t) with itself yields tri(t).

Step-by-step explanation:

The question relates to the principle of convolution in mathematics, where two functions, in this case rect(t) and tri(t), are integrated to produce a third function. According to given information, if rect(t) is convolved with itself, the result is tri(t).

Now, to answer what the result of rect(t - 1) * rect(t - 2) would be, we consider the properties of convolutions. When a rectangle function is shifted and then convolved with another shifted rectangle function, the result is a triangle function that is also shifted.

Therefore, based on the initial relationship, the convolution of rect(t - 1) with rect(t - 2) would produce a triangle function shifted accordingly, which is tri(t - 3).