How to combine the discrete bands of x-values to a continous plot?

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I require a pcolor plot showing x-values in non-linear scale. These are discrete bands with increasing values. I would like to club all the discrete bands shown in the figure and make a continous structure.
In the figure, the Y-scale is continous and have a repeated gap between the numbers, while the x-scale does not have a regular gap between the numbers. If we take a regular gap, most of the plot will be white space. How to avoid this white space and make a continous plot?
Any suggestions will be greatly appriciated.
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MP
MP 2022년 7월 11일
Thank you for your reply. Please chcek attached data.
X-axis, X.mat. (time series data)
Y-axis, Y.mat.
Colorbar, C.mat.

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KSSV
KSSV 2022년 7월 11일
load('X.mat') ;
load('Y.mat') ;
load('C.mat') ;
X = T_mag3 ;
Y = E3(1,:)' ;
Z = FESA3 ;
pcolor(X,Y,Z)
shading interp
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MP
MP 2022년 7월 11일
Oh sorry. That did not make a lot difference.
Actually, if you observed X-values, you can see that there is a narrow band from
3.57 to 3.61 (index: 1-14)
Then there a gap, then again a narrow band from
4.20 to 4.25 (index: 15-29)
Then there a gap, then again a narrow band from
12.63 to 12.70 (index: 31-54)
and so on,... This is how I want to stack distinct bands side-by-side but in a continous mode without (white/colored) gap.

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