integration troubleshooting for multiple variable functions

Hi Everyone

My problem is the following

I need to perform the following integration, with respect to z :

E3(t,deltaT)=integral of(E1(t-Zz-deltaT)*E2(t+Zz)*dz)

where E1,E2,t,z,deltaT are row vectors, whose size is roughly 2*10^5 samples, while Z cap is a scalar.

The integration range is (-inf,+inf), and the output E3 should be a function of the absolute time t and the lag deltaT.

As you can see, 1st and 2nd integrands are functions of 3 and 2 variables, respectively

I would be grateful if you can give me some feedback/ hints in order to overcome this problem

Best,

Stefano