MATLAB implementation Spline Fitting

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Check the attached problem please. I am a beginner in spline fitting and have a few questions:

1) How to find the coefficients c[n]. Is it by DTFT? 2) I understand how to find the derivative but not sure about how to deal with fractional translation? 3) What's the right function in matlab to obtain the (discrete) samples of a uniform spline function

Thanks!