# 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)