list manipulation - Convolve two sets of (x,y) data sets

I have two sets of data in the form

a={{.1,2},{.2,3},{.3,4},{.5,6}}


b={{0,8},{.1,4},{.2,7},{.3,1},{.5,10},{.6,3}}

Both data sets have even spacing, although the b dataset has significantly many more data points at higher and lower values of x. How do I convolve these data sets?

Convolve[a,b] only works if I use just the y values of the datasets. Is there a way to convolve this data while still keeping these x values?