Convolution theorem and laplace transforms

In summary, the conversation discusses the Convolution Theorem and the confusion surrounding its application in Laplace transforms. The conversation highlights the incorrect assumption that the symbol '*' represents multiplication, when in fact it represents convolution. The confusion is resolved when it is understood that the integration step is necessary in order to properly apply the Convolution Theorem.
  • #1
indianaronald
21
0
Okay, so this is the first time I'm encountering this theorem and I'm not very strong in calculus. But I tried to understand it myself but couldn't.

Convolution theorem is the one in the attachment as give in the book ( couldn't find a way to type that out easily). My doubt is if laplace(f) = F(s) and laplace(g) = G(s) and laplace( f*g )= F(s)*G(s), why not
laplace-inverse[ F(s)*G(s) ]=f*g, which is given but why do the integration at all after that? ( but my answers don;t match if I do it this way; that is without that final integration so I'm obviously misunderstanding it)

Thank you very much for any help.
 

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  • #2
Damn. I understand. What is there to understand anyway? It is not really multiplication at all. The symbol stands for 'convolution'. I can't delete this thread. So umm...it's going to be my beacon of stupidity, I guess, thank you very much.
 

FAQ: Convolution theorem and laplace transforms

1. What is the convolution theorem?

The convolution theorem is a mathematical concept that states that the convolution of two functions in the time domain is equal to the product of their respective Laplace transforms in the frequency domain.

2. What is a Laplace transform?

A Laplace transform is a mathematical tool used to convert a function from the time domain to the frequency domain. It is often used in engineering and physics to simplify differential equations and analyze systems in the frequency domain.

3. How is the convolution theorem used in signal processing?

The convolution theorem is used in signal processing to simplify the analysis of systems with time-varying inputs. By taking the Laplace transform of the input signal and the system's impulse response, the convolution theorem allows us to easily calculate the output signal in the frequency domain.

4. What are the applications of the convolution theorem?

The convolution theorem has various applications in mathematics, engineering, and physics. It is commonly used in signal processing, control theory, and system analysis. It is also used in image and audio processing, as well as in the analysis of electrical circuits.

5. Can the convolution theorem be extended to more than two functions?

Yes, the convolution theorem can be extended to an arbitrary number of functions. This is known as the generalized convolution theorem. It states that the convolution of multiple functions in the time domain is equal to the product of their respective Laplace transforms in the frequency domain.

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