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Compute Discrete-Time Fourier Transforms
Discrete-time Fourier transform gallery.
In[1]:=

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problems = {HoldForm[

    FourierSequenceTransform[DiscreteDelta[n], n, \[Omega]]], 

   HoldForm[FourierSequenceTransform[1, n, \[Omega]]], 

   HoldForm[FourierSequenceTransform[E^(I a n), n, \[Omega]]], 

   HoldForm[FourierSequenceTransform[a^n UnitStep[n], n, \[Omega]]], 

   HoldForm[

    FourierSequenceTransform[(n + 1) a^n UnitStep[n], n, \[Omega]]], 

   HoldForm[FourierSequenceTransform[Cos[n], n, \[Omega]]]};
In[2]:=

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FormulaGallery[forms_List] := 

  Module[{vals = ParallelMap[ReleaseHold, forms]}, 

   Text@TraditionalForm@

     Grid[Table[{forms[[i]], "==", vals[[i]]}, {i, Length[forms]}], 

      Dividers -> {{True, False, False, True}, All}, 

      Alignment -> {{Right, Center, Left}, Baseline}, 

      Background -> LightYellow, Spacings -> {3, 3}]];
In[3]:=

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FormulaGallery[problems]
Out[3]=