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SetOptions[FourierTransform,FourierParameters{1,-1}];
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(*Q6*)(*H(t)istheunitstepfunction.thereforethisisanaccumulator*)
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xt[τ_]=Piecewise[{{0,τ<1||τ>3},{1,3>τ>1}}];(*INPUT*)ht[τ_]:=UnitStep[τ](*ImpulseResponseH(t)*)yt[τ_]:=Convolve[ht[x],xt[x],x,τ]Plot[yt[τ],{τ,-10,10},PlotRangeAll]
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Manipulate[Show[Plot[{ht[(t-τ)],xt[τ]},{τ,-10,10},PlotRangeAll,PlotStyle{Orange,Black,Dashed},FillingBottom,PlotLabelStyle[StringForm["Convolved value at t = ``, y [ t ] = ``",t,N[yt[t],2]],Red,Bold,Larger]],Plot[yt[c],{c,-10,t}]],{{t,1.1},-5,7}]
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Convolve[ht[τ],xt[τ],τ,y]
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(*Plot[xt[τ]-yt[τ],{τ,-5,5},PlotRangeAll]*)