Interpolate function against time

Question

I have two vectors called lammdaWind11 and timeWind11. They are of size 51*1. I have interpolted each one independently as

lammdaWind11I = ListInterpolation[lammdaWind11];

and

timeWind11I = ListInterpolation[timeWind11];

However, I can find the values compared to the element of the vector. I want to put the time vector in the X axis and the lammda as the y variable so that I can know the value of the function for a certain time, not for an element of the vector. Unfortunately, I cannot find naything about this in the documentation. Can someone please tell me how to do it?

Answer 1

Some fake data

SeedRandom[42];
timeWind11=MovingAverage[Sort@RandomReal[1,51+9],10];
lammdaWind11=MovingAverage[RandomReal[1,51+9],10];

your current interpolations

lammdaWind11I = ListInterpolation[lammdaWind11];

timeWind11I = ListInterpolation[timeWind11];

Show[
ListPlot[{timeWind11,lammdaWind11},PlotStyle->{Red,Blue},PlotTheme->"Scientific"],
Plot[Evaluate@{timeWind11I[n],lammdaWind11I[n]},{n,1,51},PlotStyle->Thin]
]

My proposed solution uses Interpolation and arranges the data to the correct format using Transpose

if=Interpolation[Transpose@{timeWind11,lammdaWind11}];

Show[
 ListPlot[
  Transpose@{timeWind11,lammdaWind11}
  ,Joined->False
  ,PlotTheme->"Scientific"
 ],
 Plot[if[t],{t,Sequence@@MinMax[timeWind11]}]
]