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lugita15
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Derivative of a Convolution
How do I find the derivative of a convolution, meaning [tex]\frac{d}{dt}(f \ast g)(t)[/tex]?
[tex](f \ast g)(t)=\int^{}_{} f(t-\tau)g(\tau)d\tau[/tex]
I want to use the fundamental theorem of calculus, but I can't just directly substitute t for [tex]\tau[/tex], because that would make[tex]f(t-\tau)g(\tau)=f(0)g(t)[/tex], which doesn't make sense. How would I correctly apply the fundamental theorem of calculus in this case?
Homework Statement
How do I find the derivative of a convolution, meaning [tex]\frac{d}{dt}(f \ast g)(t)[/tex]?
Homework Equations
[tex](f \ast g)(t)=\int^{}_{} f(t-\tau)g(\tau)d\tau[/tex]
The Attempt at a Solution
I want to use the fundamental theorem of calculus, but I can't just directly substitute t for [tex]\tau[/tex], because that would make[tex]f(t-\tau)g(\tau)=f(0)g(t)[/tex], which doesn't make sense. How would I correctly apply the fundamental theorem of calculus in this case?
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