Export Animation with Arbitrary Parameter Pairs

Question

I have several functions f_i[a,b,x] I would like to export as an .avi file. They should be plotted with x as the variable and multiple arbitrary parameter pairs {{a1,b1},{a2,b2},...} of the animation. What I tried so far:

Export ["testfile.avi", Table[Table[{
Plot[Sin[(a + x/2)*x], {x, 0, 30}],
Plot[Cos[(a + x/2)*x], {x, 5, 30}],
Plot[b*Cos[(a + x/2)*x + b], {x, 5, 30}]}], {a, 0.1, 1, 0.1}]]

This gives an .avi file where the parameter a is run from 0.1 to 1 in steps of 0.1. However, I would like to have an .avi file, where the plots with the arbitrary parameter pairs {{a1,b1},{a2,b2},...} are displayed in the individual frames. How is the syntax for this?

I do have a table of the parameter pairs in Excel. Is there any way to import them conviniently?

P.S.:The actual functions are a bit more complicated, so this is a simplified example in case you are wondering.

Answer 1

You can us

 Export ["testfile.avi", frames1] (* or *)
 Export ["testfile.avi", frames2]

where frames1 is obtained using Join on the output of nested Tables:

frames1 = Join @@ Table[Table[{Plot[Sin[(a + x/2)*x], {x, 0, 30}], 
  Plot[Cos[(a + x/2)*x], {x, 5, 30}], Plot[b*Cos[(a + x/2)*x + b], {x, 5, 30}]}, 
  {b, .1, 1, .1}], 
  {a, 0.1, 1, 0.1}];

and frames2 is obtained using a single Table with a 2D iterator:

frames2 = Table[{Plot[Sin[(ab[[1]] + x/2)*x], {x, 0, 30}], 
    Plot[Cos[(ab[[1]] + x/2)*x], {x, 5, 30}], 
    Plot[ab[[2]]*Cos[(ab[[1]] + x/2)*x + ab[[2]]], {x, 5, 30}]}, {ab, 
    Tuples[Range[0.1, 1., 0.1], 2]}];

frames1 == frames2

True