Brief Explanation of Maths behind Software Defined Radio demodulation

Note in the AM LabView simulation I forgot to multiply each signal by 2 so the net signal is half the amplitude but makes no difference to the theory. (this is why when the signal is zero amplitude m=0 we get 0.5 instead of 1). This is a LabView simulation of a SDR at the final demodulation end. I show the basic maths behind how it works. I am suing the free version of LabView so anybody can have a go if they are inclined.