Δt=.;ω=.;
A[ω_]=Integrate[(1/π)(1/(Δt))Cos[ω t],{t,-Δt/2,Δt/2}]

Interaktivní zobrazení frekvenčního spektra pro obdélníkový puls

Manipulate[
Plot[{((2 Sin[((Δt ω)/2)])/(Δt π ω))},
{ω,0,50},PlotRange->{-1/4,1/2},PlotStyle->Black,AxesLabel->{"ω","B(ω)"}]
,Item[Style["4.12 Fourierova analýza",Bold,14],Alignment->Center]
,Delimiter
,Item["B(ω) = (2/π) (∫_0^∞) f(t) cos ωt \[DifferentialD]t = \!\(\*FractionBox[\(\(\\ \)\(2  sin \((\*FractionBox[\(ω\), \(2\)] Δt)\)\)\), \(π\\ Δt\\ ω\)]\),",Alignment->Center]
,Delimiter
,Item["kde f(t) = (1/(Δt)) pro -((Δt)/2) ≤ t ≤ ((Δt)/2), jinak 0"]
,Delimiter
,{{Δt,0.4,"Δt"},0.1,2}
,ControlPlacement->Left
]

Export

p=Plot[{((2 Sin[((Δt ω)/2)])/(Δt π ω))}/.{Δt->0.6},
{ω,0,50},PlotRange->{-0.2,0.4},PlotStyle->Black,AxesLabel->{"ω","B(ω)"},LabelStyle->Medium,ImageSize->400]

Export["4.12.png",p]

Signál uříznutého spektra

A[ω_]=Integrate[(1/π)(1/(Δt))Cos[ω t],{t,-Δt/2,Δt/2}]

Amod[ω_]=A[ω]Piecewise[{{1,ω<((2π)/(Δt))}},0]

Plot[Amod[ω]/.Δt->1,{ω,0,25},PlotStyle->Black,AxesLabel->{"ω","B(ω)"},LabelStyle->Medium,PlotRange->All,ImageSize->400]

f[t_]=Integrate[Amod[ω]Cos[ω t],{ω,0,∞},Assumptions->Δt>0]

Plot[{f[t]/.Δt->1,Piecewise[{{(1/(Δt)),Abs[t]≤Δt}},0]/.Δt->1},{t,-5,5},PlotRange->All,PlotStyle->{{Thick,Black},{Thin,Dashed,Gray}},Ticks->False,AxesLabel->{"t","f(t), (Subscript[f, mod])(t)"},LabelStyle->Directive[20]]