- #1
zezima1
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Determine the confolution of f with itself where f is:
f(t) = 1 for ltl<1 and 0 everywhere else
Then deduce that:
∫-∞∞ sin2ω/ω2 dω = ∏
Fouriertransform of f gives:
f(ω) = 2/√(2∏) sin(ω)/ω
and using the convolution theorem gives:
f*f = 4/√(2∏) sin2(ω)/ω2
But I'm clueless of what to do from this point. Should I evaluate the convolution integral and equate that to the above?
In that case we have:
f*f = ∫-∞∞ f(τ)f(t-τ) dτ
But how do I evaluate that? I can see that τ must be between -1 and 1. Thus t must be between -2 and 2? But what does that make the integral look like?
f(t) = 1 for ltl<1 and 0 everywhere else
Then deduce that:
∫-∞∞ sin2ω/ω2 dω = ∏
Fouriertransform of f gives:
f(ω) = 2/√(2∏) sin(ω)/ω
and using the convolution theorem gives:
f*f = 4/√(2∏) sin2(ω)/ω2
But I'm clueless of what to do from this point. Should I evaluate the convolution integral and equate that to the above?
In that case we have:
f*f = ∫-∞∞ f(τ)f(t-τ) dτ
But how do I evaluate that? I can see that τ must be between -1 and 1. Thus t must be between -2 and 2? But what does that make the integral look like?
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