WOLFRAM|DEMONSTRATIONS PROJECT

Convolutions of Shifted Densities

t

-1

s

1

density function f

Gaussian

uniform

tent

parabolic

density function g

Gaussian

uniform

tent

parabolic

The convolution of the two functions,

f

and

g

, is the function

(f*g)(τ)=

∞

∫

-∞

f(t)g(τ-t)dt

.

The plot shows

f(τ-t)

in blue,

g(τ-s)

in purple, and their convolution in gold.

This Demonstration shows how the convolution is affected when those two functions are shifted:

f(τ)f(τ-t)

and

g(τ)g(τ-s)

.