I have three sinewaves, of different periods and swings. Hows does one synthesis these sinewaves. Synthesis defintion : the combining of the constituent elements of separate material or abstract entities into a single or unified entity A simple average of the three or something else??

Very simple. Either Add, Subtract, Multiply, Divide, or apply any combining function you can think up. The first four are the most common techniques employed. A more proper way to address the question, is how does one combine different sine waves to synthesize one complex sine series? If you are dealing with fourier analysis for instance, you assume the combined complex series is comprised of a summation of series, but there's no reason they can not be combined in a different manner; the result of any of the approaches can always be expressed as a linear summation.

So just add the data points up and divide by 3. Then ! As axis is 1 to -1 guess that would work.. Just wanted to check if engineers has some special wiz bang approach...

It's not that tough You can get software which also lets you quantify angles so angle 1< angle 1b angle 3 > angle 3b And then write your equations using whatever language is at your disposal.

I'm assuming you want the overall wave form generated by the summation of the waves shown. Assuming you have actual numeric values for the horizontal axis, you can simply find the period of each wave (the distance between two identical points on the wave) and use the formula: A(t) = sin(2*pi/T1) + sin(2*pi/T2) + sin(2*pi/T3) since the amplitudes are identical (=1), pi=3.14159 and T is the period of the individual wave.

That simple. No matter how whiz bang you want to make it, it's not necessary. Only reason you would divide by 3 is to force the vertical amplitudes to be bounded to that scale of -1 to 1, but you could just as easily leave it alone, or normalize to any other scale.