Associative property of convolution

Click For Summary
The discussion centers on proving the associative property of convolution for finite intervals, contrasting with existing literature that focuses on infinite intervals. A user points out an error in the original approach, specifically regarding the misuse of the variable bounds in the integrals. They suggest applying the Fubini theorem correctly after a specific equation, emphasizing that simply switching integral signs is insufficient. Another participant seeks resources on the Fubini theorem when integration variables are involved and asks for guidance on its application in their proof. The conversation highlights the need for clarity in mathematical proofs involving convolution and integration techniques.
sainistar
Messages
3
Reaction score
0
Hi There

The associative property of convolution is proved in literature for infinite interval. I want to prove the associative property of convolution for finite interval. I have explained the problem in the attached pdf file.

Any help is appreciated.

Regards
Aman
 

Attachments

Physics news on Phys.org
Integral (10) is obviously wrong. Your two integrals have \theta in their bounds. But \theta is an integration variable! This can't be correct.

Why do you obtain something wrong here. Because after equation (3) they applied Fubini and switched the both integrals, and THEN they did the substitution.

You must do something similar. Apply Fubini after (9). But Fubini will in this case not be simply switching the integral signs...
 
Thanks micromass

I was looking for the Fubini theorem when the bound are the integration variable. I did not find any. Can you please let me know any source i can read.
It will also be helpful if you can suggest how can i apply Fubini after (9).

Regards
 

Similar threads

Undergrad Partial Derivative of Convolution
  • · Replies 2 ·
Replies
2
Views
3K
Semigroup property for convolution
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Integral of Dirac function from 0 to a.... value
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Construction of reals through Dedekind cuts in Baby Rudin
  • · Replies 1 ·
Replies
1
Views
1K
Can the Least Squares Method be expressed as a convolution?
  • · Replies 0 ·
Replies
0
Views
1K
Problem in Convolution integral by fourier transformation
  • · Replies 3 ·
Replies
3
Views
2K
Engineering Image Processing: Convolution vs Filtering
  • · Replies 1 ·
Replies
1
Views
1K
Engineering How to find the impulse function?
  • · Replies 2 ·
Replies
2
Views
2K
Simplifying Convolution Properties: Understanding the Delta Dirac Function
  • · Replies 2 ·
Replies
2
Views
2K
Convolution of two delta functions in frequency domain
  • · Replies 2 ·
Replies
2
Views
22K