Convolution area property derivation

Click For Summary
The discussion focuses on deriving the area property of convolution, specifically showing that the area under the convolution y(t) of two functions x(t) and h(t) equals the product of their individual areas. A user shares a derivation that omits a crucial step regarding the separation of integrals. The main question revolves around the process of exchanging the order of integration in the convolution definition. Clarification is sought on the mathematical justification for this step in the derivation. Understanding this concept is essential for grasping the area property in convolution.
mafra
Messages
9
Reaction score
0

Homework Statement


Let y(t) be the convolution of x(t) with h(t), show that the area under y(t) is the product of the areas under x(t) and h(t)

Homework Equations


Convolution definition

The Attempt at a Solution


I found a derivation but it skips a step, uploaded it here:
htt p://i50.tiny pic.com/s15dus.jpg
 
Physics news on Phys.org
What's the step that you were wondering about?

s15dus.jpg
 
I don't get how it is possible to separate the integrals in "exchanging the order of integration"
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Verify Green's Formula for a Simple DE
  • · Replies 1 ·
Replies
1
Views
1K
Convolution Integral Properties
  • · Replies 14 ·
Replies
14
Views
2K
Convolution Calculation (piecewise function)
  • · Replies 11 ·
Replies
11
Views
7K
MATLAB Convolution: Finding the Convolution of Two Functions with Step Inputs
  • · Replies 1 ·
Replies
1
Views
1K
Analytic solution of a Convolution Integral
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Partial Derivative of Convolution
  • · Replies 2 ·
Replies
2
Views
3K
Convolution and Transfer Function
  • · Replies 23 ·
Replies
23
Views
3K
Heat Kernel at t=0: Dirac Delta Intuition
  • · Replies 3 ·
Replies
3
Views
2K
Applying Partial Fractions to Solve Laplace Transform Convolution
  • · Replies 2 ·
Replies
2
Views
1K
Inverse Laplace : with Convolution
  • · Replies 2 ·
Replies
2
Views
1K