Signal Theory

As illustrated in Figure 5.2, the convolution of two functions f and g is defined as the integral176 of the product of one function with a reversed and shifted instance of the other

(f ∗ g)(t) , ∫ +∞ −∞

f(τ)g(t− τ)dτ = ∫ +∞ −∞

f(−τ)g(t+ τ)dτ (5.5)

while its generalization to d dimensions reads

(f ∗ g)(t1, . . . , td) , ∫ +∞ −∞

. . .