Convolution area property derivation

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SUMMARY

The discussion focuses on the derivation of the area property of convolution, specifically demonstrating that the area under the convolution y(t) of two functions x(t) and h(t) equals the product of their individual areas. The key concept involves the definition of convolution and the manipulation of integrals. A user expressed confusion regarding the step of exchanging the order of integration in the derivation process, highlighting the importance of understanding this mathematical technique.

PREREQUISITES
  • Understanding of convolution in signal processing
  • Familiarity with integral calculus
  • Knowledge of properties of definite integrals
  • Experience with mathematical proofs and derivations
NEXT STEPS
  • Study the properties of convolution in signal processing
  • Learn about Fubini's Theorem for exchanging the order of integration
  • Explore examples of convolution with different functions
  • Review integral calculus techniques relevant to convolution
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Students and professionals in electrical engineering, applied mathematics, and signal processing who are looking to deepen their understanding of convolution and its properties.

mafra
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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"
 

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