Δω=.;ω0=.;t=.;
Integrate[(1/(Δω))Cos[ω t],{ω,ω0-((Δω)/2),ω0+((Δω)/2)}]

Interaktivní vlnový balík

Manipulate[
Plot[{((2 Cos[t ω0] Sin[((dω t)/2)])/(dω t)),2/(dω t),-2/(dω t),2((Sin[dω t/2])/(dω t)),-2((Sin[dω t/2])/(dω t))},
{t,-50,50},PlotRange->{-1,1},PlotStyle->{Black,{Gray,Dotted},{Gray,Dotted},{Gray,Dashed},{Gray,Dashed}}]
,Item[Style["4.11 Fourierova analýza",Bold,14],Alignment->Center]
,Delimiter
,Item["f(t) = (∫_0^∞) B(ω) cos ωt \[DifferentialD]ω = \!\(\*FractionBox[\(\(\\ \)\(2  sin \((\*FractionBox[\(Δω\), \(2\)] t)\)\)\), \(Δω\)]\)cos((Subscript[ω, 0])t)",Alignment->Center]
,Delimiter
,Item[Dynamic[
Plot[Piecewise[{{1/dω,ω0-dω/2≤y≤ω0+dω/2}},0],{y,0,12},
PlotRange->{{0,12},{0,3}},PlotStyle->Black,Exclusions->None,AxesLabel->{"ω","B(ω)"},Ticks->{{{ω0,"(Subscript[ω, 0])"}},{{1/dω,"(1/(Δω))"}}}]
],Alignment->Center]
,Item["B(ω) = (1/(Δω)) pro (Subscript[ω, 0]) - ((Δω)/2) ≤ ω ≤ (Subscript[ω, 0]) + ((Δω)/2), jinak 0"]
,Delimiter
,{{ω0,3,"(Subscript[ω, 0])"},0,10}
,{{dω,0.4,"Δω"},0.1,2}
,ControlPlacement->Left
]

Export grafů

ω0=3;
dω=0.4;
p1=Plot[{((2 Cos[t ω0] Sin[((dω t)/2)])/(dω t)),2/(dω t),-2/(dω t),2((Sin[dω t/2])/(dω t)),-2((Sin[dω t/2])/(dω t))},
{t,-50,50},PlotRange->{-1.2,1.2},PlotStyle->{Black,{Gray,Dotted},{Gray,Dotted},{Gray,Dashed},{Gray,Dashed}},
ImageSize->500,AxesLabel->{"t","f(t)"},LabelStyle->Medium,Ticks->None,PlotPoints->100]

p2=Plot[((2 Cos[t ω0] Sin[((dω t)/2)])/(dω t)),
{t,-50,50},PlotRange->{-1.2,1.2},PlotStyle->Black,
ImageSize->500,AxesLabel->{"t","f(t)"},LabelStyle->Medium,Ticks->None,PlotPoints->100]

Export["4.11a.png",p1]
Export["4.11b.png",p2]