Convolutions of Shifted Densities
Convolutions of Shifted Densities
The convolution of the two functions, and , is the function .
f
g
(f*g)(τ)=f(t)g(τ-t)dt
∞
∫
-∞
The plot shows in blue, in purple, and their convolution in gold.
f(τ-t)
g(τ-s)
This Demonstration shows how the convolution is affected when those two functions are shifted: and .
f(τ)f(τ-t)
g(τ)g(τ-s)