About the derivation in firls.m

[je suis]

Hello everyone

And I hope this isn't the wrong list to send this to. I am trying to
make a small program in C++ about filter design, and I am currently
trying the least-squares algorithm, based on Selesnick's paper (the
same one from firls.m). However, I would like to be able to also make
type iii and iv filters, differentiators and Hilbert transformers,
too, and I was looking through your firls.m file, where I got stuck at
the derivation of "cos_ints2". If it's not too much to ask, can
someone please let me know how did it get from the formula in the
comment to the one in the function calculating "cos_ints2"? I can't
figure it out, not even with wxMaxima by my side.

In the extreme case that my beginner programming skills allow it, I
would also like to be able to make the weights as a linear variable
function, too, so I would guess that the q vector will follow about
the same principles as the b vector, so I would like to try it out,
even if my small program, most probably, will never leave the screen
of my monitor. But, if I get "lucky" (one is allowed to dream), I will
let you know.

Vlad