Least square problem and filtering

Hi! I'm having a bit of a struggle here with a least squares problem: I've got the equation k*p_dot = delta_q. Re-written into the linear parameter form of z = theta'*phi(z is p_dot, phi is delta_q and k is theta').

k is my unknown constant, I have samples for both p(not p_dot - to use derivative on p leads nowhere as the result is impossible to interpret) and delta_q. In order to get rid off p_dot I try to filter the equation by a stable filter lambda(s). The equation after laplace transform:

k(s)*p(s)*s=delta_q(s). The filter is lambda(s) and is simply set to s+1. The question is how do I implement this filter(s+1) in my equation in matlab?

All variables are vectors and sampling is [1:1:3597]

Thanks!