Adding two tables with same x axis

Question

I make two tables,gaussian and pedestal:

σ = 150;
x0 = 10;
x1 = 1;
x2 = 20;
ped1 = 15;
ped2 = 40; 
Gauss[x_] := E^(-(x - x0)^2/(2 σ^2));
gaussian = Table[{x, N[Gauss[x]]}, {x, x1, x2}]

{{1, 0.998202}, {2, 0.998579}, {3, 0.998912}, {4, 0.9992}, {5, 
  0.999445}, {6, 0.999645}, {7, 0.9998}, {8, 0.999911}, {9, 
  0.999978}, {10, 1.}, {11, 0.999978}, {12, 0.999911}, {13, 
  0.9998}, {14, 0.999645}, {15, 0.999445}, {16, 0.9992}, {17, 
  0.998912}, {18, 0.998579}, {19, 0.998202}, {20, 0.99778}}

pedestal = Table[{y, 1}, {y, ped1, ped2}]

{{15, 1}, {16, 1}, {17, 1}, {18, 1}, {19, 1}, {20, 1}, {21, 1}, {22, 
  1}, {23, 1}, {24, 1}, {25, 1}, {26, 1}, {27, 1}, {28, 1}, {29, 
  1}, {30, 1}, {31, 1}, {32, 1}, {33, 1}, {34, 1}, {35, 1}, {36, 
  1}, {37, 1}, {38, 1}, {39, 1}, {40, 1}}

I want to add gaussian and pedestal such that only the second value in each pair is added, but the x-axis stays the same. So as to result basically in a Gaussian with a uniform pedestal.

Is there a more intuitive way of doing this, without having to read out the first and second values of each list, defining the x-axis of the final plot, etc?

Can I just add the two lists with some option to only add the second entry of each tuple?

Answer 1

maybe this is what you mean?

allx = gaussian[[All, 1]]~Join~pedestal[[All, 1]] // Union
Table[ { i, 
  Total@Select[Join[gaussian, pedestal], #[[1]] == i &][[All, 
     2]] }, {i, allx}] 

or

{#[[1, 1]], Total@#[[All, 2]]} & /@ 
 GatherBy[Join[gaussian, pedestal], #[[1]] &]