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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:

∫

Fouriertransform of f gives:

f(ω) = 2/√(2∏) sin(ω)/ω

and using the convolution theorem gives:

f*f = 4/√(2∏) sin

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 = ∫

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:

∫

_{-∞}^{∞}sin^{2}ω/ω^{2}dω = ∏Fouriertransform of f gives:

f(ω) = 2/√(2∏) sin(ω)/ω

and using the convolution theorem gives:

f*f = 4/√(2∏) sin

^{2}(ω)/ω^{2}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) dτBut 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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