- #1
benndamann33
- 20
- 0
anyone know how to prove that it is commutative...
as if f *g = g*f
as if f *g = g*f
Convolution - prove commutative
- Thread starter benndamann33
- Start date
-
- Tags
- Convolution
Click For Summary
SUMMARY
The commutative property of convolution can be proven using the definitions of convolution for two functions, f and g. The convolution is defined as f*g(x) = ∫₀^∞ f(x-t)g(t)dt and g*f(x) = ∫₀^∞ g(x-u)f(u)du. By applying a change of variables, specifically substituting t with (x-u), one can demonstrate that f*g(x) equals g*f(x), confirming the commutative property.
PREREQUISITES- Understanding of convolution operations in mathematics
- Familiarity with integral calculus
- Knowledge of variable substitution techniques
- Basic concepts of function analysis
- Study the properties of convolution in signal processing
- Learn about variable substitution in integrals
- Explore the applications of convolution in Fourier transforms
- Investigate the implications of commutativity in linear systems
Mathematicians, signal processing engineers, and students studying advanced calculus or linear systems will benefit from this discussion on the commutative property of convolution.
Similar threads
- · Replies 10 ·
- · Replies 1 ·
- · Replies 2 ·
- · Replies 13 ·
- · Replies 1 ·
- · Replies 12 ·
- · Replies 2 ·
- · Replies 14 ·
- · Replies 11 ·