If you calculate a simple moving average over a window length that is equal to the period of the sinusoid, you get a straight line (=0 because the wave is symmetric around the X-axis): the wave has a period of 40, equal to the length of the window of the simple moving average: so the filter weights are 1/40, 1/40,... 40 times. This is kind of obvious because a sinusoid is like a reflection of the same shape around its axis.
Which non-trivial moving average weights would you need to find to get a filter that returns the same output as its input (so besides SMA(1) )? So I want to find the filter weights of some type of average over some window length, that when multiplied with their respective values of the sinusoid, while sliding the window over the sinusoid, add to a sum equal to the sinusoid.
ps: is it possible to answer using as little signal processing / engineering terminology as possible please? Like you're talking to a mentally challenged person.. :)