Hi, im new to this forum and i am not sure i am posting this question in the right place but here it goes.
If i have two baseband signals- u1(t) = A1(t)cos(wt+p(t)) and u2(t) = A2(t)cos(wt-p(t)),
where A1 and A2 are the amplitude changes in time in its band(which is 100 MHz for example) and p(t) is the phase changes in time in their band.
both signals reside in frequency - w. so they basicly overlap if put together.
now we multiply the first on the second and filter out the low frequencies - so basicly we receive
A1(t)*A2(t)cos(2wt).

my question is this- if i mentally divide u1 by half (take the first 50 MHz of the band) and u2 by half and then multiply all 4 halfs between themselves (and take hgher frequencies) will i receive the initial output - A1(t)*A2(t)cos(2wt)?

Thanks in advance.