Dvojrozměrná Fourierova transformace

<<Calculus`FourierTransform`

$FourierFrequencyConstant=-2 Pi

s[t1_,t2_]=Exp[-Pi t1 t1] Cos[2Pi v0 t2];

FourierTransform[s[t1,t2],{t1,t2},{v1,v2}]

Cancel[%]

s[t1_,t2_]=Exp[2Pi I(a1 t1+a2 t2)];

FourierTransform[s[t1,t2],{t1,t2},{v1,v2}]

ab[x_]=x  UnitStep[x]-x  UnitStep[-x];

Plot[ab[x],{x,-1,1}]

s[t1_,t2_]=f[t2] Exp[-Abs[t1]];

FourierTransform[s[t1,t2],{t1,t2},{v1,v2}]

Integrate[Exp[-Abs[t1]] Exp[-2Pi I t1 v1],{t1,-Infinity,Infinity},Assumptions->{Im[v1]==0}]