Cvičení 2: Konvoluce funkcí

f[x_/;x>=0]=Integrate[Exp[a*(x-s)]*Exp[b*s],{s,0,x}]
f[x_/;x<0]=0.0

a:=1;
b:=2;

Plot[f[x],{x,-2,2},PlotStyle->Thickness[0.015]]

Clear[a,b]

f[x_/;x>=0]=Integrate[Exp[a*(x-s)]*Exp[a*s],{s,0,x}]
f[x_/;x<0]=0.0

a:=1

Plot[f[x],{x,-2,2},PlotStyle->Thickness[0.015]]

<<Calculus`FourierTransform`

$FourierFrequencyConstant=-2 Pi

Clear[f]

Integrate[f[s] DiracDelta[s], {s, -Infinity, Infinity}]

Integrate[f[ t - s] DiracDelta[s], {s, -Infinity, Infinity}]

Integrate[f[s] DiracDelta[t - s], {s, -Infinity, Infinity}]