AM Demodulation in Tikz, how to implement a lowpass function

I want to draw the following picture in tikz. Number 1 is simple its a sin(X)*sin(Y) and Number 2 is just abs(sin(X)*sin(Y)). Number 4 is obviously easy too. A similar example could be found here:

https://github.com/PetarV-/TikZ/tree/master/Amplitude%20modulation

However, has somebody a clue how to draw Number 3? It’s basically a lowpassfiltering of the signal Number 2. Has tikz this capability? I know somebody might say, just plot it in Matlab. But it must be done in LaTeX! Of course, I can do it somehow manually in Tikz with splines etc. But it would be nice if we could get the real system’s behaviour in this picture.